Hi Lucy S.,
For (g o f)(x), we are looking for g(x) of f(x), which can also be written as g[f(x)], meaning substitute f(x) for any x in g(x).
So with g(x) = x + 5, replace all x's with f(x): g[f(x)] = f(x) + 5
And for f(x) = x2 + 2x - 6, we can substitute for f(x): g[x2 + 2x - 6] = (x2 + 2x - 6) + 5
To reiterate:
(g o f)(x) = g[f(x)]
(g o f)(x) = f(x) + 5
(g o f)(x) = (x2 + 2x - 6) + 5
(g o f)(x) = x2 + 2x - 1
I hope this helps, Joe.