These printers use the LC406BK cartridge:

Brother MFC-J 4335 DW

Brother MFC-J 4345 DW

Brother MFC-J 4345 DWXL

Brother MFC-J 4535 DW

Brother MFC-J 5855 DW

Brother MFC-J 5955 DW

Brother MFC-J 6555 DW

Brother MFC-J 6955 DW