It's essential to draw a diagram. Get the edges that lie in each plane as follows:

In the xy-plane, z = 0 and so the equation of the edge is x + 2y = 4.

In the zy-plane, x = 0 and so the equation of the edge is z + 8y = 16.

In the zx-plane, y = 0 and so the equation of the edge is 4x + z = 16.

Then it's not hard to see what the integral terminals will be for a particular order of integration.

Eg: The order dz dx dy.

The integral terminals are:

z = 0 (lower plane) to z = 16 - 8y - 4x (upper plane).

And the region of integration in the xy-plane is given by

x = 0 to x = 4 - 2 y

y = 0 to y = 2

Eg. The order dy dz dx.

y = 0 (lower plane) to y = (16 - 4x - z)/8 (upper plane)

And the region of integration in the zx-plane is given by ......