Concept:
Chemistry (Organic Chemistry) - IUPAC Nomenclature of Alkenes.
Step 1: Identify the principal functional group.
The principal functional group is the carbon-carbon double bond (C=C). This makes the compound an alkene, so the suffix will be "-ene".
Step 2: Determine the longest carbon chain containing the double bond.
The longest continuous chain of carbon atoms that includes the double bond contains 6 carbons. Therefore, the parent alkane name is hexane, and as an alkene, the parent root is "hexene".
Step 3: Number the carbon chain.
Numbering must start from the end that gives the lowest possible locants to the double bond.
If we number from left to right: $C_1-C_2-C_3(Br)=C_4(CH_3)-C_5-C_6$. The double bond is at position 3.
If we number from right to left, the double bond is also at position 3.
When the double bond position is symmetrical, we apply the lowest locant rule to the substituents.
Left to right: substituents at 3 (bromo) and 4 (methyl).
Right to left: substituents at 3 (methyl) and 4 (bromo).
According to alphabetical order, Bromo comes before Methyl, so it should get the lower number. Thus, we number from left to right to give Bromo the 3 position.
Step 4: Identify and locate the substituents.
Based on our numbering, there is a Bromine atom at Carbon-3 (3-bromo) and a Methyl group at Carbon-4 (4-methyl).
Step 5: Assemble the final IUPAC name.
Combine the substituent names in alphabetical order, followed by the parent chain and the double bond position:
3-Bromo + 4-methyl + hex-3-ene = 3-Bromo-4-methylhex-3-ene.
$$
\therefore \text{The IUPAC name is 3-Bromo-4-methylhex-3-ene.}
$$