A valid proposition is one which is a tautology.
A) Here, both sides are equivalent. Use p -> q = ¬p v q to verify. Hence, is is valid.
B) The existential quantifier is distributive over disjunction. Hence, both sides are equivalent and thus, the statement is valid.
C) Here, both sides are not equivalent since existential quantifier is not distributive over conjunction. But, it is still valid because if left side is true, then there exists an x=a such that both p(a)=T and q(a)=T. Applying existential generalisation with a as the particular element in the domain of x, the right side is true.
D) When left side is true, the right side can be false. If left side is true, this means for every x, p(x) v q(x) = T. But at the same time, the right side can be false because both p(x) and q(x) can be false for different values of x.
So, D is invalid.