= Solution
Let $R=\mathrm{CH(Me)CH_2CH_2CH_3}$. The useful disconnections are \b[benzoate formation, <carbonyl reduction> and <thiol> conjugate addition]:
$$
\begin{aligned}
\mathrm{RCH(OCOPh)CH_2CH_2SPh}
&\Leftarrow\mathrm{RCH(OH)CH_2CH_2SPh}+\mathrm{PhCOCl}\\
&\Leftarrow\mathrm{RCOCH_2CH_2SPh}\\
&\Leftarrow\mathrm{RCOCH=CH_2}+\mathrm{PhSH}.
\end{aligned}
$$
The sulfur-bearing <carbon> is the enone beta <carbon>, so this is a Michael disconnection, not attack of thiophenol on the alcohol-derived central <carbon>. Reduce the saturated <ketone> with <sodium borohydride> after installing SPh, then benzoylate the <alcohol> with <benzoyl chloride> and pyridine or a tertiary amine.
Disconnect the enone to $\mathrm{RCOCH_3}$ and formaldehyde. Kinetic deprotonation on the methyl side of the hindered unsymmetrical <ketone>, trapping with formaldehyde, and dehydration gives $\mathrm{RCOCH=CH_2}$. This order leaves the substituted $R$ side unchanged. An <alpha-methylenation>/Mannich-base-elimination variant is an equivalent way of installing the terminal enone.
Finally, $\mathrm{RCOCH_3=CH_3COCH(Me)CH_2CH_2CH_3}$ disconnects by alpha alkylation to \b[<butan-2-one> and 1-iodopropane]. Use the more substituted, ethyl-side <enolate> of <butan-2-one> for this step, rather than its usual methyl-side <kinetic enolate>; an equilibrated/regioisomerically selected <enolate> or enol derivative is required, and the desired monoalkylated <ketone> should be isolated. Three carbons from propyl iodide and one from formaldehyde increase the original four-carbon <ketone> to the required eight-carbon <alcohol>/thioether skeleton. Choosing ethyl iodide here would leave the target short by one <carbon>.
This is a constitutional synthesis: the target drawing specifies no configuration at either newly formed stereogenic site, so no unproved stereoselective reduction or alkylation is needed. Regioisomeric <enolate alkylation> and competing overalkylation are the practical selectivity issues to control, rather than something that follows from writing “base”.
\Image[/past-exam-of-the-chemistry-course-of-the-year-3-of-the-natural-sciences-course-of-the-university-of-cambridge/2022/paper-1-q5-disconnections.png]
{title=Original atom-counted retrosynthetic sequence from the benzoate/thioether target back to butan-2-one}
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