Answer:
Children
Step-by-step explanation:
An antecedent is a word, phrase or clause that a pronoun refers to. "Their" is a third-person plural person, thus, its antecedent should match this characteristic. In the options, the only possible antecedents are "dog" and "children" because "Its" and "theirs" are pronouns.
"Dog" is a third-person-singular son the pronouns that would match it best would be "she", "her", "he", "his", "it" or "its".
"Children", on the other hand, is in third-person plural (They), thus pronouns like "their", "them" and "they" perfectly match this antecedent.