In grammar, the word "he" and "him" are both pronouns that refer to one masculine individual; however, "he" is a subject pronoun which means it is used as a subject while "him" is an object pronoun and therefore it is used as an indirect or direct object (entity affected by the verb). This implies in the case of the sentence "The doctor and _____ talked for quite some time" the word "he" should be used instead of "him" because in this case, the word that should be placed to complete the sentence is a subject that along with "The doctor" carry out the action "talked" and therefore "he" is appropriate because this is a subject pronoun and therefore acts as subject.
