The IUPAC name for the following compound is:

Step 1: Determine Principal Functional Group Between the carboxylic acid ($\ce{-COOH}$) and the aldehyde ($\ce{-CHO}$), the carboxylic acid has higher priority. The parent chain must start from the acid group.

Step 2: Numbering and Chain

1. Numbering begins at $\ce{-COOH}$.
2. The longest chain containing the double bond and the other carbonyl has 6 carbons $\rightarrow$ Hex-3-enoic acid.

Step 3: Substituents

• C2: Methyl group.
• C5: Methyl group.
• C6: Carbonyl group (aldehyde carbon) $\rightarrow$ Named as "oxo" when part of the chain.

Step 4: Final IUPAC Name 2,5-Dimethyl-6-oxohex-3-enoic acid.

$\boxed{\text{Answer: (c) 2,5-Dimethyl-6-oxo-hex-3-enoic acid}}$