Identify the parent structure: The molecule is a benzene ring, which is the parent hydrocarbon for naming.
Identify the substituents attached to the benzene ring: There are two substituents, bromine (Br) and iodine (I).
Number the benzene ring to give the substituents the lowest possible numbers: Start numbering from the substituent that comes first alphabetically to give it position 1. Between 'bromo' and 'iodo', 'bromo' comes first alphabetically.
Assign numbers to the substituents accordingly: Bromine gets position 1, and iodine gets position 4 (para position) on the benzene ring.
Write the systematic name by listing substituents alphabetically with their position numbers: The correct name is 1-bromo-4-iodobenzene.