Prove tautology using propositional equivalence and the laws of logic determine q ∧ ( p → ¬q) → ¬p
q ∧ ( ¬p ∨ ¬q) → ¬p
(q ∧ ¬p)∨ (q ∧ ¬q) → ¬p
(q ∧ ¬p)∨ F → ¬p

i dont know how to solve this further. Kind of leaves me confused 
what would be the next step

First, a term like $P \lor F$ is equivalent to just $P$. So, as the next step you get:
$(q \land \neg p) \to \neg p$
And now rewrite this second implication just as you did the first. That is, the next step is:
$\neg (q \land \neg p) \lor \neg p$
Now do DeMorgan and you're almost there!
