I'm looking for some guidance in solving this. I have read through my text multiple times trying to find something similar to this and I'm coming up with nothing. I'm not really sure where to start on solving this problem.

The question simply states

Prove that ${{n}\choose{k}} = {{n - 2}\choose{k}} + 2{{n - 2}\choose{k - 1}} + {{n - 2}\choose{k - 2}}$.

I'm very new to binomial coefficients, and extremely lost.