At a party, everyone shook hands with everybody else. there were 66 handshakes. how many people were at the party?

This is a question that needs a bit of common sense to get to the actual answer that is desired. Firstly there is one information given .The other information has to be found from common sense. ! single handshake requires 2 people. Now we can easily determine the number of people doing 66 handshakes.
Then
The number of people required for 1 hand shake = 2
Then
The number of people required to do 66 handshakes = ( 2 * 66) people
                                                                                     = 132 people
Then it can be said that there were 132 people in the party. I hope the process of doing this problem is clear to you.

2xy/9 is the answer to this problem