To solve this problem, we need to consider two cases: selecting 4 letters with exactly 2 Gs and selecting 4 letters with exactly 3 Gs.

Case 1: Exactly 2 Gs

We choose 2 Gs from the 3 available Gs. The remaining 2 letters must be chosen from the letters A, E, R, T. The possible combinations are:

• GG with AA
• GG with AE
• GG with EE
• GG with RA
• GG with RE
• GG with RT
• GG with TA
• GG with TE

This gives us 8 ways.

Case 2: Exactly 3 Gs

We choose 3 Gs from the 3 available Gs. The remaining letter must be chosen from A, E, R, T. The possible combinations are:

• GGG with A
• GGG with E
• GGG with R
• GGG with T

This gives us 4 ways.

Total

\(Adding both cases together, we have a total of 8 + 4 = 12 ways.\)