= Solution
\b[B gives spectrum 4.] Number the unsaturated acyl chain from its <carbonyl> <carbon>. For $\mathrm{MeO-C(=O)-CH=CH-CH_3}$, the assignments are
$$
\delta_C(\mathrm{C=O})=166.9,\quad
\delta_C(\alpha\text{-CH})=122.5,\quad
\delta_C(\beta\text{-CH})=144.6,\quad
\delta_C(\mathrm{CH_3})=17.9,\quad
\delta_C(\mathrm{OCH_3})=51.3\ \mathrm{ppm}.
$$
The strongly deshielded beta <carbon> and relatively shielded alpha <carbon> reflect polarization of the <conjugated ester>. All four protonated carbons here are CH or methyl environments and share one <attached proton test> phase, whereas the <carbonyl> has the opposite phase. The methoxy <resonance> is decisive: B has an O-bound methyl, not an O-bound methylene.
\Image[/past-exam-of-the-chemistry-course-of-the-year-1-of-the-natural-sciences-course-of-the-university-of-cambridge/2023/paper-1-ester-carbons.png]
{title=Original carbon-assignment structures for B and C, showing the distinction between a conjugated acyl group and an allyl alcohol-derived group}
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