hey best friends. for a flip-flop hub, what is the greatest difference in teeth the dropouts can accommodate?

eh different bikes have different lengths

about 4cm

Figure you need some room to move the axle forward to remove the chain from the chainring so you can remove the wheel, and some room at the rear so the axle nut washer is in full contact with the dropout. So, you probably have about 1" of usable dropout travel. Your axle moves approximately 1/8" for a one tooth change in the cog, so that will allow about an 8 tooth difference, provided your chain is the correct length for the particular range of cogs you are using.