Tricky Tennis Twins

3 sets of twin sisters are married to 3 sets of twin brothers such that for any pair of twin sisters, their husbands are also twins. They then decide to have a tennis playoff. However, they require mixed pairs (1 male and 1 female) for the match but cannot have a twin and their spouse (husband or wife) as part of their team nor can they have their twin's spouse.

How many different sets of 6 mixed pairs teams are possible?

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