You can test this yourself, just cut up the cross into 6 segments and paste into the corresponding area, and you will notice that on the left side of the front box is labeled right and right is label left and when you switch it, it is labeled correctly.
The pictures I attached shows when I put left into the right slot and right into left slot the skybox setup is ok as shown on the picture. When I put left into left slot, right will be on the left side of front, when I put left into right slot then left is on the left side of the front box which is now correct. The pictures shows are after I put left into right and right into left slot.