Alright, I'll try to walk you though this:

¬ [(p -> ¬q) ^ (p v q)]

because of ¬(p^q)=¬p v ¬q we get

¬ (p -> ¬q) v ¬(p v q)

because of ¬(p->q)=p^¬q we get

(p ^ ¬¬q) ^ ¬(p v q)

because of ¬(p v q)=¬p^¬q we get

(p ^ ¬¬q) ^ (¬p ^ ¬q)

From there we just simplify and get:

(p ^ q) ^ (¬p ^ ¬q)

Hope that helps!