This is counting how many ways can you permute four people into two buckets, the two buckets of handshakers, where you care about which bucket they are in, whether they're handshaker number one or handshaker number two. This would count, this would count A being the number one handshaker and B being the number two handshaker as being different than B being the number one handshaker and A being the number two handshaker. But we don't want both of these things to occur. We don't want A to shake B's hand where A is facing north and B is facing south, and then another time, they need to shake hands again where now B is facing north and A is facing south. We only have to do it once. These are actually the same thing, so no reason for both of these to occur. So we are going to be double counting.