We need to select four letters from the word COPENHAGEN such that there is an equal number of Es and Ns, with at least one of each.

The word COPENHAGEN contains the letters: C, O, P, E, N, H, A, G, E, N.

There are 2 Es and 2 Ns in the word.

First, consider the case where we select one E and one N. We need to choose 2 more letters from the remaining 6 letters (C, O, P, H, A, G).

The number of ways to choose 2 letters from these 6 is given by the combination formula:

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

So, there are 15 ways to select EN**.

Next, consider the case where we select both Es and both Ns (EENN). There is only 1 way to do this.

Therefore, the total number of different selections is:

\(15 + 1 = 16\)