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When integrating with respect to z first, I had the limits such that z ranged from 2x^2-4 to 4-2y^2, and since x and y only depend on z and z has been covered already, I thought that x and y both ranged from -2 to 2.

When I integrated with respect to z last, I had x range from -(z/2+2)^1/2 to (z/2+2)^1/2 and y range from -(2-z/2)^1/2 to (2-z/2)^1/2, with z ranging from -4 to 4.

The problem is that I got two different answers, although I feel more confident in my answer from integrating the second way, z last (128/3). Could anyone help me with where I went wrong?