Stuck on combinatorial proof that $\binom{w}{p} \binom{p}{m} = \binom{w}{m} \binom{w-m}{p-m}$

Question

I'm in an introductory discrete mathematics course and i'm having a lot of trouble with this proof. I'm not sure if i'm heading in the right direction or not but I used the fact that $\binom{n}{k} = \frac{n!}{k!(n-k)!}$ and started trying to algebraically reduce them to eachother but haven't succeeded. Any help would be much appreciated.