Hi, here's how I did it:
~(p → ~q) ∨ ( q ∧ ( p ∨ ¬ q))
This is the statement you've started with. We can build a truth table to show that ~(p → ~q) ≡ (p ∧ q) (try this yourself!). This gives us
(p ∧ q) ∨ ( q ∧ ( p ∨ ¬ q))
Now, by the associative law, we can regroup the parentheses to get
p ∧ (q ∨ ( q ∧ ( p ∨ ¬ q)))
Notice here that in the parentheses we have q ∨ (something). It doesn't really matter what that something evaluates to, since logically q or something = q. We thus have
p ∧ (q)
which is what we needed to show.
Hope that helps! Let me know if you have any questions.