are you talking about elongating the chain? Like taking propanoic acid (3 carbons) and making it n-butanol (4 carbons)?
Based on the answer given I think we're looking at adding to the carbonyl with a carbon nucleophile, followed by reduction of the resulting ketone to the secondary alcohol.
my proposed solution is esterificating it, then add organometallic reagent to the ester.
is there a shorter method? and is my proposed solution correct?
You're on the right track, however, as Azmanam has pointed out, you will probably have problems with over-addition to the carbonyl. Problem is that the ketone you want to generate is more reactive than the ester you started with, so you will get a second addition of your organometallic reagent.
I see two options.
1. Instead of an ester, can you think of a carboxylic acid derivative that is more reactive than a ketone? This will help to control single addition, giving a ketone.
Once you have your ketone, how do you propose to reduce it to the alcohol?
2. Do the reduction first. How could you reduce your carboxylic acid to an aldehyde (more than one step may be required)?
Once you have your aldehyde, you can then add your organometallic and get your secondary alcohol.