OP.
You're on the right track so far, what you need to do is equate your two expressions for y.
So x^2 - 4 = x + 2
Now, bring these all to one side x^2 - x - 6 = 0
Now, you can either factorise in your head, or if you're really not sure, use the quadratic formula,
With your values of x, substitute them into an expression of y and see what you get!