Which pronoun correctly completes the sentence: Both you and he ___ should play golf more often?

The correct pronoun to complete the sentence is "he." In this context, the structure of the sentence requires a subject pronoun because both "you" and "he" are the subjects of the implied action (playing golf).

The sentence is using the conjunction "and" to connect two subjects, making it clear that the action is being taken by both "you" and "he." Therefore, the pronoun that follows must also be in the subject form, which is "he."

Using "him," "they," or "she" wouldn't fit because "him" is an object pronoun and does not indicate the subject performing the action. "They" is a plural pronoun, which departs from the singular context of "you" and "he," and "she" introduces a different person instead of referencing "he." Thus, "he" is the appropriate choice to maintain grammatical consistency and correctness in the sentence.