What is the IUPAC name for

The structure is:

      CH2-CH3
      |
CH3-CH2-CH=C-CH3

We can trace two possible main chains containing the double bond:

• Chain 1: $\text{CH}_3-\text{CH}_2-\text{CH}=\text{C}-\text{CH}_3$. This chain has 5 carbons (pentene). If this were the main chain, the $\text{CH}_2\text{CH}_3$ group would be an ethyl substituent.
• Chain 2: $\text{CH}_3-\text{CH}_2-\text{CH}=\text{C}-(\text{CH}_2-\text{CH}_3)$. This chain has 6 carbons (hexene). If this were the main chain, the $\text{CH}_3$ group would be a methyl substituent.

According to IUPAC rules, the longest chain containing the double bond is the parent chain. Therefore, the 6-carbon chain (hexene) is the parent chain.

The parent chain is $\text{CH}_3-\text{CH}_2-\text{CH}=\text{C}-\text{CH}_2-\text{CH}_3$.
The methyl group is attached to one of the carbons of the double bond.

• Numbering from left to right: $\text{C}1\text{H}_3-\text{C}2\text{H}_2-\text{C}3\text{H}=\text{C}4-\text{C}5\text{H}_2-\text{C}6\text{H}_3$ The double bond is between C3 and C4 (starting at C3). The methyl group is on C4.
• Numbering from right to left: $\text{C}6\text{H}_3-\text{C}5\text{H}_2-\text{C}4\text{H}=\text{C}3-\text{C}2\text{H}_2-\text{C}1\text{H}_3$ The double bond is between C3 and C4 (starting at C3). The methyl group is on C3.

Both numbering schemes give the double bond the same position (starting at C3). In such cases, we choose the numbering that gives the substituent the lowest number.

• Left-to-right numbering: Methyl at C4.
• Right-to-left numbering: Methyl at C3. Since 3 is lower than 4, the right-to-left numbering is correct.

The parent chain is a 6-carbon alkene with a double bond starting at position 3, so it's "hex-3-ene".
There is a methyl group at position 3.
Combining these, the name is 3-methylhex-3-ene.

Comparing this with the given options:
A. 4-ethylpent-3-ene
B. 2-ethylpent-2-ene
C. 3-methylhex-3-ene
D. 4-methylhex-3-ene

The correct option is C.

The final answer is $\boxed{\text{C. 3-methylhex-3-ene}}$.