Discrete math - negate proposition using the quantifier negation

Question

I'm asked to negate the following proposition using the quantifier negation rules. No negation operations are to appear before any of the quantifiers in the expression that is created. The issue is I'm not quite understanding what this means. All I'm given in my notes relating to negation quantifiers are the following formulas and their proofs:

∃xP(x)=¬∀x¬P(x)

∀xP(x)=¬∃x¬P(x)

I'm not quite sure how to take this information and apply it to a proposition or really, I don't quite understand what my end goal of this question is supposed to be.

This is the proposition I'm given to work with. I'd appreciate if someone taught me step by step how to solve these types of questions. You can make up your own proposition if you'd like, but I'm really confused and would appreciate some sort of example. The results I found online seemed really complex and confusing.

Given proposition:

∃ (() → (() ∨ F(x)))

Answer 1

Hint

You have to negate it, i.e. to put the negation sign : $\lnot$ in front of the formula, to get :

$\lnot \ [∃x (D(x) → (C(x) \lor F(x)))]$

and then "move inside" the negation sign using the above equivalences between quantifiers.

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From : $∃xP(x) \equiv ¬∀x¬P(x)$ we get : $¬ ∃xP(x) \equiv ¬¬ ∀x¬P(x)$ and thus, using Double Negation :

$¬ ∃xP(x) \equiv ∀x¬P(x)$