If in doubt, draw a tree. The four branches of the tree are WW, WR, RW and RR, but we're told that the first counter chosen is white so we only need to bother with the WW and WR branches.
At the start, there are 7 white counters and n red counters.
For the first choice, P(W) = 7/(n + 7). Can you continue from there to find P(WW) and P(WR)?
After that, you need to look further at P(WW) and P(WR) to see which of them yields an integer solution for n. (You will be solving quadratics in n).