 Solution

Hydride removes the remaining alpha proton at the substituted benzylic carbon, releasing hydrogen and forming the conjugated enolate. Its oxygen attacks the carbonyl carbon of allyl chloroformate. Collapse of the tetrahedral intermediate expels chloride and gives the allyl enol carbonate, with the double bond between the original carbonyl carbon and the cyanomethyl-bearing carbon.

This is O-acylation of an enolate: the carbonyl oxygen is trapped as $\mathrm{OC}{\mathrm{O}}_2\mathrm{C}{\mathrm{H}}_2\mathrm{CH}=\mathrm{C}{\mathrm{H}}_2$, retaining the enol double bond. The competing carbon-centred resonance representation explains possible C-acylation in other circumstances, but it would give a different connectivity from E. The indicated product selects the oxygen-trapping pathway and the conjugated enolate regioisomer.