Hello,
Since the rear triangle on that folding bike prevents the front derailleur from moving totally to the inside, the chain rubs slightly against the derailleur's fork when on the inner ring. No biggie, but a silent bike is nice.

To add a spacer on the drive side and move the bottom bracket axle a bit to the right, I thus need to undo the BB (plastic) cups. Worth trying before buying a BB with a longer axle.

Before using more force, do you confirm 1) it's the right tool, and 2) it's the usual threading on both sides (lefty loosey)?

Thank you.

Nope. One side has left hand threads and one doesn't.

I had same problem on Dahon Speed 2X conversion, front derailleur cage would hit on front derailleur adaptor, due to its thickness and huge diameter seat tube, cage not far enough inboard to shift to the small ring. So I spaced BB out 4mm. Worked, but kept dropping chain, and this is a 2 piece crank so left crank arm then had 4mm less clamping length, came loose. Then fixed proper:

Removed spacers, now chainline is perfect like the biking gods intended, not constantly dropping chain when shifting to low chainring when on low cog.

Inner lip on front derailleur was massive overkill, thick metal and a large lip width. Marked area where it interfered, and with a 4" angle grinder, ground just that area off, almost to flush. Was still plenty stiff. Put front derailleur back on, adjusted, has worked flawlessly for two years, a lot of miles, a lot of shifts.

For you, you don't need to take as much off. Just enough to allow you to adjust your derailleur limit screw to allow the cage to go in just a hair more.

Threads: PEDALS are right hand thread on right, left hand on left.

Standard (BSA) bottom bracket is reverse, Right hand thread on left, left hand thread on right.

It's easy to remember if you're a bit contrary by nature-------

Right is left, and left is right.

That looks like a nice version of the tool. Be sure to loosen the locknut immediately after breaking it free.

If muscle power doesn't do it, try impact on the wrench handle with a dead-blow mallet. Also try a heat gun/hair dryer on the metal shell, after protecting or removing plastic parts.

Generally only the left side uses plastic retaining cups. One trick to reduce their breakage possibility is to loosen the right/drive side first. This reduces the force needed to remove the plastic cup.

BTW "Before using more force, do you confirm 1) it's the right tool, and 2) it's the usual threading on both sides (lefty loosey)?" could be miss understood by some. My answers might be yes, do confirm the tool and threading before using the tool. Andy (fighting the trend to minimize verbiage which also increases ambiguity)

I would recommend the new BB or replace the plastic cup with a metal one. Having seen a few broken plastic cups in my day and not liking to see them again getting a new B.B. or just a metal cup would be the way to go.

As others have said that is the tool and right is left and left is right.

Plastic cups work fine if you aren't a klutz with tools. Trying to replace a plastic cup with a metal one might create issues.

In my Ti MTB I've had a cheap BB with two plastic cups for a couple decades. Completely proof against galvanic corrosion.

I'll add that I've seen quite a few LH plastic BB retaining cups/rings that are/were cracked and the BB and bike worked just fine. Including one of my own that saw many thousands of miles after the install (when the crack happened...) If the BB was otherwise well installed and the cups stay tight the crack is likely to be a "no big deal", till it's removed.

Generally, I much prefer metal to plastic for fittings (and frames but that's another topic). But there are some applications of plastic in bikes that work quite well. Andy

So on a British BB, the right cup comes loose by turning clockwise. But it still wouldn't budge: Turned out I should start by loosening the left-side cup (turn anti-clockwise, as usual).

As for the BB shell (68mm wide): ID ~33,5mm OD ~40mm. I'll look around to find a set of spacers to find one that matches, before either going medieval on the inner lip with an angle grinder or getting a BB with a longer axle (current: 127mm.)

Thanks all.

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.

But there's no way to know which side is flanged and thus should be removed last.

Spacers: Curiously, when I decided to space my BB out 4mm, I had some spacers I had bought once to space the cassette out (decided against, due to greatly reduced lockring thread depth), and I'll be darned if those spacer ID and OD were the exact size to space out the BB. That's gotta be pure accident, as BSA BBs predate Shimano freehub bodies by half a century.

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.

The flange is visible when installed.

Left is right and right is wrong.

No need. The axle spins with the tool in place. There isn’t any binding as the bottom bracket comes out.

Rather than try to remember which cup is left threaded and which is right threaded, I’ve found that people remember how to remove the cups easier if they are instructed to push down on the wrench when it is at the 3 o’clock position as in the picture below. This works for both sides which is what makes it easy to remember.

If you push down with the wrench at 3 o'clock on the left side you'll be turning it clockwise and tightening it.

So that's not useful.

You probably meant push down when the wrench is pointing at the front hub.

Use your eyes. If there's a flange it'll be visible, as is the one in the photo of your BB. If there's no visible flange it's because there is none.

BBs with flanges have them as a reference point, where it's tightened against the shell to locate the unit, with the unflanged
side tightened against the cartridge.

Indeed. Once entirelly removed from the bike, it's obvious there's a flange only on the drive-side.

Is it not equally obvious while installed?

I started from the drive side and didn't check the non-drive side

Have a good day