The extension of Wilson's theorem mentioned in 6.20 is the result from problem 6.9. The main idea is just pairing up a number k with (p-k) in (p-1)!. Try writing out for an example like p=5 or p=13.

Note that problem 6.29 is also asking about this same result. So you could also explore what happens for p = 7 or p = 9 (which should both fail) to try to understand what happens there too.