The IUPAC name of the compound is (a) 6-bromo-2-chlorocyclohexene (b) 3-bromo-1-chlorocyclohexene (c) 1 -bromo-3-chlorocyclohexene (d) 2-bromo-6-chlorocyclohexene

In this case, the parent chain is cyclohexene, which is a 6-membered ring with one double bond. All of the options have this as their base name, so we can continue to the next step.

We have two substituents: bromine (Br) and chlorine (Cl). According to IUPAC naming rules, the lower locant number should be assigned to the substituent nearest to the double bond of cyclohexene. If there is a tie, then the alphabetical order should break that tie. We analyze each option: (a) 6-bromo-2-chlorocyclohexene: Here, bromine is at the 6th position, and chlorine is at the 2nd position. (b) 3-bromo-1-chlorocyclohexene: Bromine is at the 3rd position and chlorine is at the 1st position. In this case, the chlorine is closest to the double bond, which is preferable according to the naming rules. (c) 1-bromo-3-chlorocyclohexene: Bromine is at the 1st position, and chlorine is at the 3rd position. Here, bromine is closest to the double bond. (d) 2-bromo-6-chlorocyclohexene: Bromine is at the 2nd position, and chlorine is at the 6th position.

After analyzing the numbers assigned to the substituents in each option and checking the alphabetical order rule, the correct choice should be (c) 1-bromo-3-chlorocyclohexene. In this option, the bromine is closest to the double bond and it is also consistent with alphabetical order rules. So, the IUPAC name of the given compound is 1-bromo-3-chlorocyclohexene.