My countryside has a famous the moutain.

or "Where I live in the countryside, there is a famous mountain"

It is far from city center, about 10 kilometers.

I go to visit there once a year.

Either "I go there" or "I visit there"

You can climb the moutain by foot or go to the top of the moutain by cable car.

You don't need to repeat "of the mountain" as we already know that is what you are talking about

My countryside has a famous the moutain.

It is far from the city center, about 10 kilometers.

I go to visit ithere once a year.

My countryside has a famous the mountain.

It far from city center at about 10 kilometer.s.

I go to visit ithere once a year.