I've listened a lecture of Tedto a TedTalk for two days, the lecture was discussing how physical exercise take has benefits for the brain,.

The neuroscientist presented that exercise is the most transformative thing people could do for their brain for the following three reasons.

Studies have shown that a single workout will improve your reaction times, which basically means you are going to be faster at catching that cup ofat Starbucks asif it falls off the counter.

But these effects are transient, they helped only right after.

What people need to do is to change their exercise regime, such as increase the cardiorespiratory function to get a long-lasting effects, because the workout could actually produces brand new brain cells in the hippocampus.

Number two, long-term exercise ihas improved attention function dependent on your prefrontal cortex.

People not only get better focus and attention but the volumes of the hippocampus increases as well.

How physical movement eactivity affect ons your brain

I think “physical activity” sounds more natural. Alternatively, you could just say “movement” (because by using “movement”, you’re implying that its physical)

“Effect” is the noun, and “affect(s)” is the verb form. If you use the verb, you don’t need to use “on” afterwards.

Alternatively, if you wanted to use the noun “effect”, you could say something like “the effects of physical activity on your brain”.

As an additional note, because it’s a title you could capitalise the words, but in this context where it’s not a published article or anything I don’t really think it’s too important. If this was in a more formal scientific article though, I’d suggest changing “your brain” to “the brain”.

I've listened a lecture of Ted for two days, the lectureFor two days, I've been listening to a TED Talk which was discussing how physical exercise take activity benefit fors the brain,.

I put “for two days” at the beginning of the sentence to clarify the meaning of the sentence and to avoid repeating “lecture” to keep the sentence shorter (which is also the reason for “which”).

How you use “listening”, “listened”, etc. in this sentence depends on exactly what you wanted to communicate with it (because I understood it one way, but in trying to explain it I realised that there were a lot of variations which worked, but they each changed the meaning of the sentence slightly). So could you possibly elaborate on it with some vague details like how long ago you listened to it or when you finished listening to it so I can try to better correct it and provide an explanation?

You need to use “to” after “listen” if you’re specifying what you’re listening to (but if you’re just listening in general, such as to what someone is saying in a conversation to show that you are paying attention, then you could just say “I’m listening”).

I think you meant “TED Talk” but I’m not 100% sure (I could just be really ignorant right now).

Like “movement”, “exercise” also implies that it is physical so you could either say “exercise” or “physical activity”.

I think using “benefit” as a verb here (so “benefits” sounds a little better and more natural here.
If you really wanted to use “benefit” as a noun though, I think “has” would work better than “takes” here (so it would become “how exercise/physical activity has benefits for the brain”, though that still sounds weird to me)

The neuroscientist presentesuggested/put forward that exercise is the most transformative thing people could do for their brain for the following three reasons.

Using “presented that” in this way sounds unnatural to me for some reason, so you could either change “presented” to something else like I’ve suggested, or alternatively you could shift the whole sentence to something more like “the neuroscientist presented exercise as being the most transformative thing people could do…”

Number one,: a single workout could immediately increase your levels of transmitters, which improves your mood right after the workout.

Studies have shown that a single workout will improve your reaction times, which basically means you are going to be faster at catching that cup of Starbucks as it falls off the counter.

“Reaction time” is usually used instead of “times” in a general sense (opposed to something like specific results from an experiment) here

But these effects are transient,; they helped right after.

I think this would be the correct use of a semicolon, but to be honest I’m not entirely certain. But I think if you wanted to use a comma, you’d need to add in some other words to better connect the two clauses. I’d recommend some more in depth research into punctuation like colons and semicolons though.

What people need to do is to change their exercise regime, such as increase their cardiorespiratory function to get a long-lasting effects, because the workout could actually produces brand new brain cells in the hippocampus.

The “to” is unnecessary at the beginning of the sentence.

“Such as increase” feels slightly weird to me, but I’m not sure why or how to change it.

I changed “the” to “their” so it kind of matches how you say “change their exercise regime”. Alternatively you could just omit “the” entirely.

You can’t use “a” with a plural (so it’s either “a long lasting effect” or “long lasting effects”.

Because you’ve used “could” in that clause at the end, you can just say “produce” without the ‘s’.

Number two,: long-term exercise is improveds attention functionwhich is dependent on your prefrontal cortex.

“Is improved” would mean that the long-term exercise is what was improved instead of someone’s attention.
You could also say something like “leads to improved”, but using “improves” as a verb is a lot more concise.

You would need to say “functions” for it to make grammatical sense, so you could say “which functions dependent on…” but that feels a little clunky and unnatural to me.

You could also say “which is controlled by your prefrontal cortex” if you still wanted to fully convey the idea of “function”.

People not only get better focus and attention but the volumes of the hippocampus increases as well.

Finally, people not only get immediately effects of mood with’s mood are not only affected in the short-term, but exercise but also get long-lastingleads to long-term increases in those good mood neurotransmitters.

“Immediately” is an adverb, so it would be used with “affect” (verb) but not “effect” (noun).

I changed the rest of it for clarification

How physical movement eaffect ons your brain

I've been listened a lecture of Ted for two days, the lecture wasing to a TED lecture for the past two days, which discussinged how physical exercise take brings benefits for the brain,.

(1) "TED" is all capitalised.
(2) Alternatively, instead of "TED lecture", you can say "TED talk", which is more commonly used amongst English speakers.
(3) The phrase is "bring benefits for (someone or something)".
(4) Notice that "brings" is in the singular form as opposed to the plural form ("bring"), because "physical exercise" is singular.

The neuroscientist presentesaid that exercise is the most transformative thing people couldan do for their brains for the following three reasons.

(1) "Present" isn't very appropriate here.
(2) I find that "brains" (plural) sounds more natural than "brain" (singular)", because "people" (plural) would imply more than one brain.

Number one, a single workout couldan immediately increase your levelsthe number of transmitters in your body, which improves your mood right after the workout.

Here, "could" conveys a sense of uncertainty, while "can" is a firm assertion.

Studies have shown that a single workout will improve (your) reaction times, which basically means you are going to be faster at catching that cup of Starbucks as it falls off the counter.

(1) You can omit "your" here if you wish.
(2) "Reaction time" is singular here. It will be plural when referring to multiple people's reaction times.

But these effects are (only) transient, they helped right after.

"Helped" should be in the present tense, because you're referring to a general fact instead of a specific past event.

What people need to do is to change their exercise regime, such as increase the cardiorespiratory functionintensity to get a long-lasting effects, because the workout could actually produces brand new brain cells in the hippocampus.

(1) "Cardiorespiratory function" refers to the body, not to an exercise regime. An exercise regime does not have "cardiorespiratory functions".
(2) "Effects" is plural, so you shouldn't use "a".
(3) "Could produces" is grammatically incorrect. "Could" is already singular, so "produces" doesn't have to be. When we have a verbal phrase consisting of more than one word like "could produce", only the first word needs to indicate whether it is singular or plural.

Number two, long-term exercise is improveds attention functionspan, which is dependent on your prefrontal cortex.

The phrase is "attention span" or just "attention".

People nNot only do you get better focus and attention, but the volumes of theyour hippocampus increases as well.

(1) Instead of "people", I'd use "you" instead for consistency, as you also used "your" in the previous sentence.
(2) I think shifting "not only" to the front of this sentence sounds more fluent.
(3) The hippocampus has only one volume because it is only one single object.

Finally, people not only getexperience immediately effects ofn mood with exercise but also get long-lasting increases in the number of those good mood neurotransmitters.

(1) I think "experience" might sound better here instead of "get".
(2) "Immediately" is an adverb. "Immediate" is the adjective.