[vivekrai]

I'm unable to proceed very much. Since Et^- is highly basic it abstracts the -COOH proton(See p1p.png). So that's all? Doesn't seem so because the problem says that the product is obtained in 65% yield.

[Fluorine]

You have three equivalents of ethyllithium, two could deprotanate (acid and alcohol) leaving the third to go for a nucleophilic attack on the carbonyl. That's how I see it proceeding.