Brother LC432 and LC432XL cartridges have authentication chip sets with unique serial numbers. This is a counter measure by Brother to try force users to only use genuine Brother. Each time you use a cartridge, it uses one of these numbers. If it tries to use a number it has used before, you’ll get an error, and the cartridge won’t work.
Compatible cartridges unique serial number can only be used once per life of the printer. It's important to keep track of the serial numbers you've used so you don't accidentally reuse one.
If you’ve only used Brother cartridges before, you don’t need to worry about this with your first purchase of non-Brother cartridges.
If you have compatible cartridges already you can inspect the cartridge box or directly on the cartridge which will have the serial number.
Shown in the picture:
A1 Is the Chip Version
432 Cartridge series
X Cartridge size
Y Colour of the cartridge BK/C/M/Y
N2 is the Serial Number
Chip Version A1 then the Serial Number N2. So if you had this cartridge A1N2 then installing another A1N2 will not work in the printer as it requires a unique number not used before. But if it was A1N3 it will work.