The IUPAC name of the given compound is

3-Bromo-4,4-dimethyl-cyclohexene

The correct answer is Option (1) → 3-Bromo-4,4-dimethyl-cyclohexene

The IUPAC name is determined by applying specific nomenclature rules for cyclic alkenes:

Step 1: Identify the Parent Chain

The parent structure is a six-membered ring with one double bond, making it cyclohexene.

Step 2: Number the Ring

For substituted cycloalkenes, the double bond carbons are always assigned positions 1 and 2. The numbering direction is chosen to give the substituents the lowest possible locants at the first point of difference.

Starting from the carbon at the bottom of the double bond and numbering clockwise: The bromine ($\text{Br}$) is at $\text{C}_3$ and the two methyl ($\text{CH}_3$) groups are at $\text{C}_4$.

If numbered the other way, the substituents would receive much higher numbers (5 and 6). Therefore, the locant set is 3, 4, 4.

Step 3: Identify and List Substituents

• Bromo group at $\text{C}_3$.
• Two methyl groups at $\text{C}_4$ (indicated by the prefix "di").
• Substituents are listed alphabetically (ignoring the "di" prefix): Bromo comes before methyl.

Step 4: Assemble the Name

Combining the parts: 3-bromo + 4,4-dimethyl + cyclohexene results in 3-Bromo-4,4-dimethyl-cyclohexene.