The two possible answers for this question are pronouns. “He” is a pronoun in the subjective case. And, “him” is a pronoun in the objective case. For a pronoun to be in the subjective case, it needs to be the doer of the action/verb. For a pronoun to be in objective case, it needs to be either a direct object, an indirect object, or an object of a preposition. In this particular sentence, “him” is correct because it is object of the preposition “of”—actually part of the compound object (brother and him).
