¿qué te gusta hacer? te gusta cocinar. me gusta cocinar. le gustas cocinar. me gusto cocinar.

This is an interrogative sentence written in present tense with the second person in singular tú (you):

¿Qué te gusta hacer?

What do you like to do?

Therefore the answer must in be present tense with the first person in singular yo (I):

Me gusta cocinar

I like to cook

The other options are incorrect because:

-Te gusta cocinar (You like to cook) is not with the first person in singular

-Le gustas cocinar is grammatically incorrect, the verb gustar (to like), conjugated with the third person in singular (the subject in this sentence) is gusta.

-Me gusto cocinar although is written with the first person in singular is grammatically incorrect because the verb gustar (to like) is conjugated in past as gustó (liked), with accent.