Originally Posted by
FBinNY
One of my favorite (mental) tools when taking apart the unfamiliar is to consider how it would have gone together.
So, here you have two cups, one flanged one not. If you stop to think, you'd see that the flanged one must go on first. Otherwise, there'd be no reference for how far the left one would go, nor to ensure the flange met the BB shell.
Once you dope out the assembly sequence, the disassembly is identical, in reverse, aka last in, first out.
The flange is external, as in your picture. There are BBs where both cups have flanges, and neither has them. But most have a flange on the right and none on the left.
Regardless of what order they were installed in, either should be okay to start with.