= Solution
Let $g:C\to D$ have the <left lifting property against monomorphisms>, and suppose $\alpha,\beta:D\to B$ satisfy $\alpha g=\beta g$. Use the <categorical diagonal> $\Delta_B:B\to B\times B$, which is a <monomorphism> by part (a). The square with top arrow $\alpha g$, bottom arrow $\langle\alpha,\beta\rangle$, left arrow $g$ and right arrow $\Delta_B$ commutes, since both product components are $\alpha g$.
Its lift $t:D\to B$ satisfies $\Delta_Bt=\langle\alpha,\beta\rangle$. Applying the two <product in a category> projections gives $t=\alpha$ and $t=\beta$. Thus \b[$g$ is an epimorphism]. This <binary-product criterion for lifting-only strong epimorphisms> requires binary products, rather than any assumption about <equalizers>.
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