I'm confused on how to talk about two people's past relationship in this sentence
"She knows about him and Frank's past" or "She knows about he and Frank's past" or "She knows about his and Frank's past"
These two people (he and Frank) were dating in the past.
The rule to follow distinguishes between joint and separate ownership. If you're talking about joint ownership, i.e., the past that both parties share, then only the second noun is possessive:
She knows about him and Frank's past.
The objective case for the third person pronoun, him, is required since it's the object of the preposition about. Unfortunately this introduces an ambiguity in that the interpretation could be
She knows about him, and she knows about Frank's past.
If you switch the order thusly:
She knows about Frank and his past.
you get another problem, as a kind commenter noted: The proximate antecedent for his is Frank, leading to the interpretation
She knows about Frank and Frank's past.
The compound nature of the shared past is more evident with two names:
She knows about Frank and John's past.
which is interpreted as
She knows about (Frank-and-John)'s past.
The past here is the shared one belonging to both Frank and John.
If you're talking about two separate pasts -- suppose Frank and he have never even met -- make both nouns possessive, and the order doesn't matter:
She knows about Frank's and his past.
She knows about his and Frank's past.
This is interpreted as
She knows about Frank's past. She knows about his past.
And for completeness:
She knows about Frank's and John's past.
She knows about John's and Frank's past
This is interpreted as
She knows about Frank's past. She knows about John's past.
