Right answer:
le gusta
In this sentence, we have two words. First, le is the indirect object pronoun that matches the third person singular. An Indirect Object Pronoun is a person that receives the action of a verb indirectly. Its purpose is to tell you to whom or for whom something is done. So the action of this sentence is being performed for Juan, that is, for him. On the other hand, since after the second blank comes an infinitive verb, then the conjugation of the verb gustar must match the third person singular, which is gusta. Finally:
¿Qué le gusta hacer a Juan en vacaciones?