Good steps on how to start integral problems involving intersecting solids?

Question

As an example, "W is the solid in the $R^3$ below the surface equation $z=2x^2 + 2y^2$ and above the R region in the xy plane bounded by the $y=x^2$ and $x=y^2$ curves. Draw R and W. Find the volume of W." It's very hard to find the limits of integration and to visualize what geometric form will output of such intersection and I think this is a very common issue with students. Thanks in advance!