Consider the two Gs that must be together as a single unit or block. This reduces the problem to arranging 8 units: GG, R, E, E, N, A, G, E.

The number of ways to arrange these 8 units is given by:

\(\frac{7!}{3!}\)

since there are 3 E's that are identical.

Now, consider the 6 possible positions for the block GG among the other letters. This gives:

\(\frac{7!}{3!} \times 6\)

Calculating this gives:

\(\frac{5040}{6} = 5040\)

Thus, there are 5040 ways to arrange the letters such that exactly two Gs are next to each other.