Which of the following reactions proceed through a carbanion intermediate formed by deprotonation (E1cB mechanism)?

E1cB occurs when a beta hydrogen is acidic and the leaving group is poor. The hydrogens alpha to the carbonyl group in the two beta-hydroxy carbonyl compounds are acidic, and hydroxide is a poor leaving group, so an enolate (carbanion) forms first and then expels $\mathrm{OH}{}^{-}$. The two alkyl bromides have good leaving groups and non-acidic hydrogens, so they react by concerted E2.