The pronoun case of the bolded word <em>him </em>is objective case. The words <em>to him </em>are used as indirect object in this sentence, which means that the case that the pronoun is used in is the objective case, or the accusative, in technical terms. The other case would be the subjective case, but given that there is no obvious subject in this sentence (it is implied), there are no subjective cases.
