Answer:
Peter and Paulette raked the leaves in their front yard.
Explanation:
Possessive pronouns show possession or ownership in a sentence. There are two types: Absolute possessive pronouns, namely, mine, yours, his, hers, its, ours, yours, and theirs. And possessive adjectives, namely, my, your, his, her, its, our, your, and their; unlike, absolute possessive pronouns, possessive adjectives are always placed next to a noun.
So, with this definition, we can easily discard option 2 "them." because it is not a possessive pronoun.
Now, in the sentence, the possessive pronoun that should be in the blank is one that refers to both Peter and Paulette, that is to say, to the third-person plural. "Her" and "his" refers to the third-person singular, and "their" refers to the third-person singular,l, so the correct answer is definitely "their."