Parent ring identification

The structure is a substituted cyclohexene ring, so the parent hydrocarbon is cyclohexene.

Rule for numbering in cycloalkenes

In a cycloalkene, the double bond must get locants 1 and 2.

So we begin numbering from one carbon of the double bond and proceed through the ring in the direction that gives the substituents the lowest set of locants.

Assign substituent positions

From the given structure, the substituents are:

• one chloro group on a double-bond carbon,
• one bromo group elsewhere on the ring.

Numbering the double bond as $1,2$ and choosing the correct direction gives:

• chloro at C-1
• bromo at C-3

Hence the locants are 1-chloro and 3-bromo.

Write substituents in alphabetical order

In IUPAC naming, substituents are written alphabetically:

• bromo before chloro

Therefore the name becomes: $3\text{-bromo}-1\text{-chlorocyclohexene}$

Check options

• A: $3$-bromo-$1$-chlorocyclohexene ✅
• B: $1$-bromo-$3$-chlorocyclohexene ❌ substituent positions interchanged
• C: $2$-bromo-$6$-chlorocyclohex-$1$-ene ❌ numbering does not give lowest locants correctly
• D: $6$-bromo-$2$-chlorocyclohexene ❌ incorrect numbering

Derived answer

The correct IUPAC name is: $\boxed{3\text{-bromo}-1\text{-chlorocyclohexene}}$