Final answer:
The missing object pronouns in the sentence are 'a él', and the correct form of the verb 'gustar' is 'encanta'.
Step-by-step explanation:
The missing object pronouns in the sequence "El libro, ¿ da a tu hermano?" would be 'a él'. The complete sentence would be: 'El libro, ¿le da a tu hermano?'. The pronoun 'le' is the indirect object pronoun used to refer to 'tu hermano' (your brother) and it is referring to a person.
The correct form of the verb 'gustar' to use in the sentence 'A mí me (encantar) viajar mucho.' would be 'encanta'. The complete sentence would be: 'A mí me encanta viajar mucho.' The verb 'gustar' is used to express likes and dislikes, and in this case, 'encanta' agrees with 'viajar mucho' (to travel a lot), the thing that is liked.
Learn more about Object pronouns, verb 'gustar'