When doing synthesis problems involving enolates (carbonyl alpha substitutions, aldol and Claisen condensations), there are some things to keep in mind:
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The alpha carbon must have been the enolate (nucleophile). So it's importnant to identify the alpha carbon!
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The bond is always made between the alpha and beta carbon.
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Beta hydroxyl products come from aldol condensations (aldehydes/ketones), beta carbonyl products come from Claisen condensations (esters/acid chlorides). (See problem 743 for these mechanisms.)
Also, α,β-unsaturated products come from β-hydroxy products, which come from aldol condensations.
After finding the alpha carbon, it's a good idea to mark the "cut" or "disconnection" where the new bond was formed. This will always be between the alph and beta carbons. I mark this with a dotted line.
a) This product is an α,β-unsaturated carbonyl, which must have come from a β-hydroxyl carbonyl. So this is an aldol condensation.
The α carbon must have come form the enolate. Because the β carbon is an alcohol, the electrophile must have been an aldehyde or ketone. So the two carbons on the right were the enolate, and the two carbons (and phenyl) on the left were an aldehyde.
b) The product is β-keto so this must have been a Claisen condensation.
The β carbon is an ketone, so the electrophile must have been an ester.
There are actually two different combinations of esters that would result in this product. I arbitrarily chose the alpha carbon to belong to the left carbonyl.
c) β-keto product so this must have been a Claisen style condensation. It's easiest if you have the alpha carbon belong to the left carbonyl, so an intramolecule reaction isn't necessary.
The β carbon is already an ester, so the electrophile had to have been more than an ester, as regular esters become ketones after a Claisen condensation.
d) This is a Robinson annulation product, which comes from an intramolecular condensation.
The α,β-unsaturated carbonyl must have come from a β-hydroxyl carbonyl. (aldol condensation)
Because the β carbon became an alcohol, the electrophile must have been an aldehyde or ketone.
