The only problem with that answer, mac, is that it doesn't use the functions he is told to use. In general it's true that f(g(x)) is not equal to g(f(x)), but then here g is specifically defined as f-inverse, so they must be equal.
I've noticed that my answer might be just a bit too general for the problem, so a better answer might be: "Yes, they must be the same. In the first case, f(g(x)), we subtract 6 from x, then halve the result, and then double that and add six to get back to where we started. In the second case, g(f(x)), we first double x, then add six, then subtract six again, and half that, so once again everything cancels and the two are the same."
Hope this helps.
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Don't use this answer, but you could also say something like: "Hang on! You're a Martian Ambassador who has travelled all the way to Earth! I doubt you managed that without knowing how inverse functions work..."