Consider two cases: twins in the team and twins out of the team.

Case 1: Twins in the team

If the twins are in the team, we need to choose 2 boys from 6 and 0 more girls from the remaining 5 girls.

The number of ways to choose 2 boys is given by:

\(\binom{6}{2} = 15\)

Case 2: Twins out of the team

If the twins are not in the team, we need to choose 2 girls from the remaining 5 girls and 2 boys from 6.

The number of ways to choose 2 girls is:

\(\binom{5}{2} = 10\)

The number of ways to choose 2 boys is:

\(\binom{6}{2} = 15\)

Thus, the total number of ways for this case is:

\(10 \times 15 = 150\)

Total number of ways

Adding both cases together, the total number of ways is:

\(15 + 150 = 165\)