TITLE: Four married couples attend a party. Each person shakes hands with every other person, except their own spouse, exactly once. How many handshakes?
QUESTION [12 upvotes]: Four married couples attend a party. Each person shakes hands with every other person, except their own spouse, exactly once. How many handshakes?

My book gave the answer as $24$. I do not understand why.

I thought of it like this:
You have four pairs of couples, so you can think of it as 
M1W2, M2W2, M3W3, M4W4, 
where
M is a man and W is a woman. M1 has to shake 6 other hands, excluding his wife. You have to do this 4 times for the other men, so you have $4\times 6$ handshakes, but in my answer, you are double counting. 
How do I approach this problem?

REPLY [3 votes]: Each line is a handshake between the required two people.  There are 24 lines: