in general though... whenever i see a beta-keto-ester as a starting reagent and a product which has only one carbonyl i tend to think of this type of reaction transformation
Good call
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Confused chiral girl, the basis of synthetic organic chemistry is building carbon skeletons. To do this we use functional groups (ketones, esters, aldehydes, double bonds, halides etc.) as "handles" to activate carbon atoms to assist in forming carbon-carbon bonds. Carbonyls are great because they help stabilise a negative charge on the carbon next to them - i.e. a strong base will generally abstract a proton next to a carbonyl group. Two carbonyls on either side of a carbon makes that even easier. Negative charges, thus generated are nucleophilic and will attack other carbonyls, alkyl halides, vinyl halides, etc.... anything that is electrophilic, to form a new carbon-carbon bond.
Finally, once you have used one of these functional group "handles" to help form your new carbon-carbon bond you might want to get rid of it. Esters can be hydrolysed to acids which can (sometimes) be decarboxylated, ketones can be reduced to alcohols and (sometimes) eliminated to give a double bond, which can in turn be hydrogenated, and so on. It's really an extensive and powerful toolbox of reactions that can be used to build up carbon frameworks. Once you understand how the tools work, you start to recognise where to use them. Like most puzzles, the easiest way is to work backwards from your solution (the product) to the starting materials. This is a whole philosopy of organic synthesis called the "disconnection approach".
As with most puzzles, you can stare at them for hours in frustration and then when you see the solution it all seems very obvious. Practice helps. Don't panic, it can be fun.