Identify the longest carbon chain in the molecule that includes the highest priority functional groups. In this case, the longest chain is an 8-carbon chain with a carboxylic acid group, making it an octanoic acid derivative.
Number the carbon chain starting from the end closest to the highest priority functional group, which is the carboxylic acid group. This makes the carboxylic acid carbon number 1.
Identify and name the substituents on the main carbon chain. Here, there is a methoxy group at carbon 8, a hydroxy group at carbon 7, and a keto group at carbon 3.
Determine the stereochemistry of the chiral centers. The hydroxy group at carbon 7 is in the R configuration, which should be indicated in the name.
Combine all the information to construct the IUPAC name: Start with the stereochemistry, followed by the substituents in alphabetical order, and finally the name of the main chain with the functional group suffix. The name should reflect the correct positions and configurations of all substituents and functional groups.