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In an E1cb elimination, deprotonation first produces a conjugate-base intermediate, followed by leaving-group loss. Dehydration of an appropriate aldol product can form a conjugated enone.

A undergoes a Robinson annulation. For an unambiguous connectivity description, call the original ring carbonyl carbon C1 and the side-chain-bearing alpha carbon C6. Label the appended chain $C6-\mathrm{a}-\mathrm{b}-\mathrm{c}(=\mathrm{O})-\mathrm{d}$, where d is initially methyl. Base makes the enolate at d, which attacks C1 intramolecularly to close the six-membered ring $C1-C6-\mathrm{a}-\mathrm{b}-\mathrm{c}-\mathrm{d}$. The carbonyl $\pi$ electrons move to oxygen, and protonation gives the beta-hydroxy ketone.

An E1cb elimination then removes the proton on d and the hydroxy group on C1, giving the conjugated enone with C1=d and a carbonyl at c. The original ring methyl remains on the carbon next to C1 on the other side. The two rings share the C1–C6 bond. The molecular formula is consistent with loss of one water molecule from the diketone.

The key sequence is deprotonation, anionic eight-pi electrocyclization, then elimination. Label the conjugated route from the lower cyclopentene to the right cyclopentene aswhere $C_3$ is the methylene joining the lower ring to the central alkene, and $C_4$ carries the $\mathrm{C}{\mathrm{H}}_2\mathrm{OC}(\mathrm{O})\mathrm{NM}{\mathrm{e}}_2$ substituent.

potassium hexamethyldisilazide removes a proton at $C_3$. The resulting anion is delocalized over the seven-carbon array: its six pi-bond electrons plus the lone pair make an eight-electron system. Thermal electrocyclic reaction is disrotatory for this $4n$ electron count. Joining $C_1$ and $C_7$ forms the seven-membered central ring and puts the remaining anionic character at $C_4$, with double bonds at $C_2=C_3$ and $C_5=C_6$.

That $C_4$ anion then forms $C_4=C{H}_2$, expelling the O-dimethylcarbamate group from the attached methylene. This E1cb elimination supplies the exocyclic methylene and explains why no oxygen remains in the depicted product. The disrotatory closure, with the cyclopentene ends folded to avoid unfavorable overlap, gives the trans relationship between the two lower fused-ring bonds shown by the wedge and dash. A simple [3,3] rearrangement would not create the required bond between the two remote cyclopentene termini.