I made a table of all four possibilities: A_coin B_coin A_guess B_guess H H ? ? H T ? ? T H

I made a table of all four possibilities: A_coin B_coin A_guess B_guess H H ? ? H T ? ? T H ? ? T T ? ? Then I tried to fill in the guesses, given that A_guess has to be based on B_coin and vice-versa. After making Alice guess the same as her coin flip, since that's a simple thing to try first, it was clear that Bob had to guess the opposite of his coin flip for each row to have exactly one correct match.