First sketch the curves, see attachment.

Now to find this area it is easier to integrate in the y-direction, so write

the curves in the form x=f(y), to get:

a) x = y^2-4

b) x = 4 - 2y

Then the area is:

A = integral_{y=-4 to 2} (4 - 2y)-(y^2-4) dy

which is elementary and you should be able to do it yourself

(its 36, which is what I get by counting squares ).

RonL