Let there be x number of man and 2 women.
Since each men play with each other the combination will be x^C_2 , but there are two games for each then 2* x^C_2
Each man plays with the two women, number of ways would be 2x.
Given 2 * x^C_2 -2x =66
integer x should lie between (b) to exceed games by 66.