There are three families each with two sons and two daughters. In how many ways can these young people be married so that each couple includes one member of each gender, no couple is brother and sister, and there are no singles left over?
Now that I've demonstrated the danger of off-the-cuff answers...
Take 3 families A, B, C
All in the family option:
BB CC AA or CC AA BB configurations
Within each of the 3 pairs there are 2 options for ordering for 2^3 options for each configuration - total 16 possibilities
BC AC AB configuration only option
Within each of the three pairs there are 2 options for order of which son marries the daughter of which family for 2^3 options
Additionally, each daughter pair can be "swapped" for 2^3 additional options within each prior option - total 8*8 = 64 possibilities
So I get a total of 80 possibilities.