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Methyl vinyl ketone is $\mathrm{C}{\mathrm{H}}_2=\mathrm{CHCOC}{\mathrm{H}}_3$, an alpha,beta-unsaturated ketone. Conjugation connects its carbon-carbon double bond with the carbonyl group.

A nucleophile can therefore react at the carbonyl carbon or through conjugate addition at the beta carbon. The product depends on the nucleophile and conditions, illustrating how conjugation creates more than one electrophilic site.

Pyrrolidine and 2-methylcyclohexanone first form an enamine, through carbonyl addition, carbinolamine formation, dehydration to an iminium ion, and alpha deprotonation. The less hindered enamine carbon is on the side opposite the methyl-bearing alpha carbon. It attacks the terminal beta carbon of methyl vinyl ketone, while the conjugated $\pi$ system shifts to oxygen. Protonation gives an alkylated iminium species; aqueous acid then hydrolyses it back to the ketone.

The result is a Michael addition product: the previously unsubstituted alpha carbon bears $-\mathrm{C}{\mathrm{H}}_2\mathrm{C}{\mathrm{H}}_2\mathrm{COC}{\mathrm{H}}_3$. In drawing the arrows, start the new C–C bond at the enamine carbon, not at nitrogen. The iminium bond is restored during addition and removed by hydrolysis. The sequence is an enamine-mediated conjugate addition, rather than direct addition to the methyl vinyl ketone carbonyl.