Which pronoun should be used in the sentence: "My brother and his fiancée were planning (his and her, their) wedding"?

The use of "their" in the sentence "My brother and his fiancée were planning their wedding" is appropriate because it acknowledges that both individuals are jointly involved in the planning of the wedding. "Their" serves as a plural possessive pronoun that encompasses both the brother and his fiancée, which accurately reflects the shared responsibility and partnership in the context of the wedding.

This option helps to avoid redundancy or awkwardness that would arise from using "his and her," which would be less fluid in terms of natural speech and writing style. While "his and her" might technically describe possession, it does not convey the sense of joint stewardship that "their" provides. The other choices would not effectively capture the collaborative nature of the event being discussed.