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First convert this to have better understanding.
"No female like a male."
$\forall x$ $\forall y$ ( (Female(x) ^ Male(y)) $\rightarrow$ ~like(x, y) )


"No female like a male who doesn't like all vegetarian".
$\forall x$ $\forall y$ $\forall z$ ( (Female(x) ^ Male(y) ^ Veg(z) ^ ~like(y, z) )  $\rightarrow$ ~like(x, y) ).


$\forall x$ $\forall y$ $\forall z$ ( ~(Female(x) ^ Male(y) ^ Veg(z) ^ ~like(y, z) )  $\vee$ ~like(x, y) ). 
As (P $\rightarrow$ Q) == (~P v Q)
Also ~(~P) = P. So we can put double negation, it can't affect.

$\forall x$ $\forall y$ $\forall z$ ~(~ ( ~(Female(x) ^ Male(y) ^ Veg(z) ^ ~like(y, z) )  $\vee$ ~like(x, y) ) ).
From here take one negation out of quantifiers and one negation inside statement. we can get this.
 ~ ($\exists x$ $\exists y$ $\exists z$ ( (Female(x) ^ Male(y) ^ Veg(z) ^ ~like(y, z) ) ^ like(x, y)).

So ans: C

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