Hello M7MBA.

Let's take a look at your question.

We have to find the value of y.

First Statement

(1) 3|x^2 - 4| = y - 2

Here we have the following equations: $$3\left(x^2-4\right)=y-2\ \ \ \ \ \ \ \ or\ \ \ \ \ \ \ \ 3\left(4-x^2\right)=y-2$$ $$3x^2-12=y-2\ \ \ \ \ \ \ \ or\ \ \ \ \ \ \ \ 12-3x^2=y-2$$ $$3x^2-10=y\ \ \ \ \ \ \ \ or\ \ \ \ \ \ \ \ 14-3x^2=y$$ So, we couldn't get a the value for y. Therefore, this statement is not sufficient.

First Statement

(2) |3 - y| = 11

Now, we have the following equations: $$3-y=11\ \ \ \ \ \ or\ \ \ \ \ \ \ 3-y=-11$$ $$y=-8\ \ \ \ \ \ or\ \ \ \ \ \ \ y=14.$$ Since we got two different values for y, then this statement is not sufficient.

First Statement + Second Statement

(1) 3|x^2 - 4| = y - 2
(2) |3 - y| = 11

First, we know from the second statement that y=-8 or y=14. Now, from the first statement we can conclude that y-2 is positive, and then y must be greater than 2, which implies that y=14.

Therefore, using both statements together is sufficient.

The correct answer is the option C.

I hope it helps.