45 is correct.
Steps :
1) Choose 4 players who will play in Game = 6C4 = 15 ways
2) Now, suppose we have 4 players {A,B,C,D} & we have to form two teams of 2.
means partition of 4 in 2,2
=> (AB - CD) , (AC - BD) , (AD - BC) = 3 ways
Total 15 * 3 = 45 ways (Ans)