jmc

Case 1: $n+6\ge 0$ $$|n+6|=n+6=2-n.$$Solve for $n$: $2n=-4,$ so we have $n=-2$.

Case 2: $n+6\le 0$ $$|n+6|=-n-6=2-n.$$Then we get $-6=2,$ which means that there are no solutions in this case.

Therefore, $n$ must be $\boxed{-2}.$