Quick help:
So this is confusing me for some reason. I don't know what rule am i missing. I feel both should equal the same no matter how you start it.
-(p → q)
= (-p → -q)
= (p ∨ -q)
or
-(p → q)
= -((-p) ∨ q)
= (p ∧ -q)
Which one is valid? and why? what rule am i missing?
There's no prescribed order for the application of rules when you want to establish an equivalence between two propositional formulas. Here are some valid equivalences that apply to the formulas you're dealing with. I'll change the variable names so you can more easily swap in your subformulas:
$$ \begin{align} \neg\,(A\to B) &\iff (A \wedge \neg B) \\ (A\to B) &\iff (\neg A \vee B) \\ \neg\,(A\wedge B) &\iff \neg A \vee \neg B \\ \neg \neg\, C &\iff C \\ \end{align} $$