= Solution
This is an \b[<Ireland–Claisen rearrangement>]. Number the <ester> <carbonyl> carbon $C_0$, its enolizable carbon $C_\alpha$, and the three allylic ring carbons $C_1-C_2=C_3$, starting at the carbon bearing the <ester> oxygen.
<lithium hexamethyldisilazide> removes an $\alpha$ <proton> and <trimethylsilyl chloride> traps the oxygen of the resulting <ester enolate>, giving a <silyl ketene acetal>. Heating permits a six-electron, \[3,3\]-<sigmatropic rearrangement> through the array
$$
C_\alpha=C_0-O-C_1-C_2=C_3.
$$
The electron-pair movements are $\pi(C_\alpha=C_0)\to C_0=O$, $\sigma(O-C_1)\to\pi(C_1=C_2)$, and $\pi(C_2=C_3)\to\sigma(C_3-C_\alpha)$. Acidic work-up cleaves the silyl <ester> to the <carboxylic acid>. The benzyl ether remains a protecting group; it is not the migrating bond.
The <suprafacial reaction> transfers the starting allylic <stereochemistry> to $C_3$, where the new side chain is delivered from the original oxygen face. In the product's printed orientation, \b[the new C$_3$–C$_\alpha$ bond is behind the ring and the C$_3$ methyl group is toward the viewer]. At that ring star, the <Cahn-Ingold-Prelog priority rules> orders the groups as side chain, alkenyl ring direction, saturated ring direction, methyl, giving \b[$R$].
The second star is $C_\alpha$. Its priorities are carboxyl, substituted ring carbon, $\mathrm{CH_2CH_2OBn}$, H. A chair-like transition state normally places the bulky side chain pseudoequatorial. However, \b[its absolute configuration also depends on the E/Z geometry of the trapped <silyl ketene acetal>]: opposite geometries give opposite configurations at this star under the same suprafacial ring transfer. The printed conditions do not state solvent or the ketene-acetal geometry. Thus the secure assignment is the ring-star $R$ configuration and conditional $\alpha$-star <stereochemistry>, rather than an unqualified absolute assignment to both stars. Drawing the assumed ketene-acetal geometry and its chair is necessary before selecting one $\alpha$ epimer.
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