Divisibility problem using Wilson's theorem: $4(p-3)! + 2$ is divisible by $p$

Question

Prove that $4(p-3)! + 2$ is divisible by $p$, where $p$ is an odd prime. Use Wilson's theorem.

I am having trouble trying to bring it in the form where Wilson's theorem can be applied.

Any help would be appreciated.

Answer 1

HINT:

$$4\cdot(p-3)!\equiv2(p-1)(p-2)\cdot(p-3)!\equiv2(p-1)!\pmod p$$