Prescript: I quoted the standard form of argument because its use of colours improves readability.
Hereafter, imagine and pretend that the conclusion were unseen and unstated. To wit, pretend that you were given only P1 to P4, from which you yourself must discover and derive the conclusion.
Because the antecedent of P2 is positive, but P3 and P4 are negations, the key idea is seemingly to apply modus tollens to P2:
5. ¬(Y or Z) ⟹ ¬(W and X).
Then apply DeMorgan's Law to distribute the negator (ie ¬):
6. ¬Y and ¬Z ⟹ ¬W or ¬X.
Now what must be done? Please explain and show all steps and thought processes.