I assume the question means: how many ways can you organise a single mixed doubles match from that pool of 12 players such that no married couple are both playing. (If instead we are organising 3 concurrent matches with the same condition then the problem is harder.)
Choose the two men in the game: 6C2.
Choose the two women in the game 4C2 (The partners of the men cannot be chosen.)
Choose way of pairing up the 4 players selected: 2