I got only one correct answer for the puzzle, from Anku Jain – Well done and thanks! Anku’s answer was better explained than the source itself, and hence taking the liberty of reproducing his answer verbatim here.

Assuming, no one follows a religion where polygamy is allowed , the answer could be as follows: There are 9 people excluding the guy asking the question as there are a total of 5 couples.The max any person can shake hands with is 8. So, the 9 people shake hands with 0,1,2 … 8 people since all of them gave different answers. For the person who shook hands with 8 people, it means all those 8 people had shaken hand at least once. So, the only person left who could have shaken 0 hands is his/her spouse. Going by the same logic, for the person who shook 7 hands, the spouse would have shaken 1 hands and so on. The other couples would be 6/2 and 5/3. So, only answer 4 is left. That’s the number of handshakes the questioner’s wife shaked..

Hope you all enjoyed the puzzle!