Double Integration of 4-y^2 in Bounded Region

[Renzokuken]

1. ∬(4-y^2 )dxdy
bounded region between y^2=2x and y^2=8-2x

I took the integral 4-y^2 dx and got 4x-xy^2 from 0-4 = 16-4y^2
then I took the integral 16-4y^2 dy from -2-2 = 128/3

It is wrong and I don't know what to do.

 

[sprint]

draw a picture of y^2=2x and y^2=8-2x on a graph and the limits of integration will become more clear

but to do that first solve for y