The correct structure of 2,6-Dimethyl-dec-4-ene is :

To determine which structure corresponds to the IUPAC name 2,6-Dimethyl-dec-4-ene, we can break down the IUPAC name systematically:

1. Parent Carbon Chain (Word Root):
The word root "dec" indicates that the longest continuous carbon chain containing the double bond has 10 carbon atoms.

2. Principal Functional Group (Primary Suffix):
The suffix "4-ene" indicates the presence of a carbon-carbon double bond ($C=C$) starting at carbon-4 (i.e., between C4 and C5).

3. Substituents (Prefix):
The prefix "2,6-Dimethyl" indicates that there are two methyl ($-{\mathrm{CH}}_3$) groups attached to the main chain at C2 and C6.

4. Analyzing the Correct Structure (Option 1 / Image 1):
If we number the longest continuous carbon chain starting from the top-right methyl group of the structure in Option 1:
• C1: The methyl group at the top-right end.
• C2: The CH carbon bonded to a methyl substituent.
• C3: The next CH₂ group.
• C4 and C5: The double-bonded carbons ($-\mathrm{CH}=\mathrm{CH}-$). This places the double bond at position 4.
• C6: The CH carbon bonded to the second methyl substituent.
• C7 to C10: The remaining four carbons ($-{\mathrm{CH}}_2-{\mathrm{CH}}_2-{\mathrm{CH}}_2-{\mathrm{CH}}_3$) at the bottom, completing the 10-carbon chain.

This numbering gives the substituents and double bond the lowest possible locants, confirming that the structure in the first image is indeed 2,6-Dimethyl-dec-4-ene.