The IUPAC name of the following compound is :

1. Principal Functional Group & Main Chain Selection:

• According to IUPAC priority rules, the carboxylic acid group ($$-\text{COOH}$$) has higher priority than the ester group. Therefore, the suffix of the compound is -oic acid, and the carbon of the $$-\text{COOH}$$ group is designated as C1.
• The longest continuous carbon chain containing the principal functional group is selected as the main chain, which consists of 6 carbon atoms (a hexanoic acid backbone).

2. Numbering and Substituents:

Numbering the chain starting from the carboxylic acid carbon (right-to-left or left-to-right as indicated in the structure):

• $$\text{C1}$$: Carbon of the $$-\text{COOH}$$ group.
• $$\text{C2}$$: $$-\text{CH}-$$ carbon bearing a methyl ($$-\text{CH}_3$$) group.
• $$\text{C3, C4}$$: $$-\text{CH}_2-\text{CH}_2-$$ linker.
• $$\text{C5}$$: $$-\text{CH}-$$ carbon bearing a methyl ($$-\text{CH}_3$$) group and a methoxycarbonyl ($$-\text{COOCH}_3$$) substituent.
• $$\text{C6}$$: Carbon of the ester group ($$-\text{COOCH}_3$$) when numbered along the main chain to name the substituent.

Thus, we have methyl substituents at positions 2 and 5, and a methoxycarbonyl substituent. Combining these gives the IUPAC name: 6-Methoxycarbonyl-2,5-dimethylhexanoic acid.

Conclusion:

The correct IUPAC name of the compound is 6-Methoxycarbonyl-2,5-dimethylhexanoic acid.

Answer: Option C