= Solution
Let $a$ be the internal vinylic <proton>, $b$ the terminal <proton> trans to $a$, $c$ the terminal <proton> cis to $a$, $d$ the oxygen-bound methylene and $e$ the chlorine-bound methylene. The assignments are
$$
\begin{array}{c|c|c|c}
\text{site}&\delta_H/\mathrm{ppm}&\text{integral}&\text{multiplicity}\\\hline
a&6.480&1&\text{doublet of doublets}\\
b&4.220&1&\text{doublet of doublets}\\
c&4.072&1&\text{doublet of doublets}\\
d&3.948&2&\text{triplet}\\
e&3.708&2&\text{triplet}
\end{array}
$$
For the $a$ <doublet of doublets>, pairing corresponding lines gives $J_{ab}\simeq300[(6.516-6.468)+(6.492-6.445)]/2=14.25$ Hz and $J_{ac}\simeq300[(6.516-6.492)+(6.468-6.445)]/2=7.05$ Hz. The larger value identifies <trans vinylic coupling>; the smaller identifies <cis vinylic coupling>. The $b$ resonance confirms the large splitting, approximately $14.25$ Hz, and has a small <geminal coupling> to $c$.
The small spacings are not perfectly reciprocal if treated as exact <First-order NMR multiplets>: the $b$ lines imply $|J_{bc}|\simeq2.55$ Hz, whereas the $c$ lines imply $|J_{bc}|\simeq2.10$ Hz and $J_{ac}\simeq6.60$ Hz. Thus report \b[$J_{ab}\simeq14.3$ Hz, $J_{ac}\simeq7$ Hz and $|J_{bc}|\simeq2$–$3$ Hz], rather than asserting incompatible exact constants. Printed precision and departures from a simple first-order pattern limit this line-picking estimate; a full spin-system fit would be needed for refined values. Splittings alone do not establish the signs of these couplings.
The two <methylene groups> split one another into approximate <NMR triplets>, with $J_{de}\simeq300(3.727-3.708)=5.7$ Hz; the oxygen-bound triplet gives approximately the same value from its rounded line labels. The three vinylic <protons> plus two methylenes give the required seven-<proton> integral. The terminal vinylic <protons> are <diastereotopic>, because replacing one or the other creates different alkene geometries.
\Image[/past-exam-of-the-chemistry-course-of-the-year-1-of-the-natural-sciences-course-of-the-university-of-cambridge/2022/paper-1-vinylether-assignment.png]
{title=Original carbon and separate proton assignments for C, including trans, cis, geminal and methylene coupling paths}
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