Answer: Objective.
Explanation: a possessive pronoun is a pronoun that indicates possession (for example mine, yours, hers, theirs, his, etc). Nominative pronouns are the ones that usually act as the subject of a sentence (for example: I, you, he, she, it, they, and we), and objective pronouns are the ones that are normally used either as the direct or indirect object of a verb, or as the object of a preposition (for example: him, her, them, etc). In the given sentence the correct pronoun to use is an objective pronoun (him/her).
