IUPAC name is

The correct option is 3-Ethyl-1,1-dimethyl cyclohexane.

To determine the correct IUPAC name of the given organic compound, we follow the standard IUPAC nomenclature rules for cyclic alkanes:
1. Identify the parent ring: The main structure is a six-membered saturated carbon ring, which corresponds to the parent name cyclohexane.
2. Identify the substituents:
- At one position on the ring, there are two methyl groups (−CH₃), forming a gem-dimethyl group.
- At another position, there is a two-carbon chain, which is an ethyl substituent (−CH₂CH₃).

3. Number the ring (Lowest Locant Rule):
We assign position numbers to the ring carbons such that the set of locants (the position numbers of the substituents) is as low as possible at the first point of difference:
- Path A: If we number the carbon containing the two methyl groups as Carbon-1, and proceed towards the ethyl group, the locants for the substituents are at positions 1, 1, and 3. This gives the set of locants: (1, 1, 3).
- Path B: If we number the carbon containing the ethyl group as Carbon-1, and proceed towards the methyl groups, the locants for the substituents are at positions 1, 3, and 3. This gives the set of locants: (1, 3, 3).

Comparing the two sets of locants term-by-term:
- The first locant is 1 in both sets: (1, 1, 3) vs (1, 3, 3).
- The second locant is 1 in Path A and 3 in Path B: (1, 1, 3) vs (1, 3, 3). Since 1 is lower than 3, the set (1, 1, 3) is preferred.
Consequently, as shown in the labeled image, the carbon with the two methyl groups is assigned as Carbon-1, and the carbon with the ethyl group is Carbon-3.

4. Alphabetical Ordering:
When writing the final IUPAC name, the substituents must be listed in alphabetical order. Note that prefixes indicating multiplicity (such as "di-") are ignored for alphabetical comparison:
- "ethyl" (starts with 'e') comes alphabetically before "methyl" (starts with 'm').
- Therefore, the ethyl group at position 3 is listed first, followed by the two methyl groups at position 1.

Combining all these parts, the IUPAC name is:
3-Ethyl-1,1-dimethyl cyclohexane