I do not remember too much grammar, but I think that in this case it is the "que", plus question, which commands a subjunctive. You may say: ¿Te gusta hacer alguna otra cosa? Sé lo que te gusta hacer. and both sound natural, but when you put a "que", and you are asking then you need a subjunctive. Hope that someone who remember the grammar may answer correctly.

It is because you are asking as if saying is there something you may like. your asking if there is a possibility that there is something she/he may like