= Solution
Both side chains have the order \b[ring–$\mathrm{CH_2CH=CHMe}$], and both printed double bonds have the Z geometry. The two <carbon> side chains are cis to one another; equivalently the labelled ring H and ring Me are cis on the opposite face. A useful common late precursor therefore has two cis \b[ring–$\mathrm{CH_2CHO}$] substituents, which can undergo two Z-selective ethylidene Wittig reactions.
Use the starting 2-methylcyclohex-2-en-1-one in a \b[reductive alpha-alkylation]. Conjugate reduction under dissolving-metal/enolate-trapping conditions, followed by a primary <electrophile> $\mathrm{BrCH_2CH_2OTBS}$, installs a protected two-carbon <alcohol> side chain at the original methyl-bearing alpha <carbon>. This gives 2-methyl-2-(2-siloxyethyl)cyclohexanone. The <carbon> at that position is now quaternary, with its original methyl retained. Alternatively, reduce the enone to 2-methylcyclohexanone and deliberately form/select its more substituted <enolate> before alkylation; its opposite <kinetic enolate> would give the wrong regioisomer.
Convert the remaining ring <ketone> to an exocyclic enoate by Horner–Wadsworth–Emmons <olefination> with a <phosphonoacetate>:
$$
\mathrm{ring\ C=O\longrightarrow ring\ C=CHCO_2Et}.
$$
Hydrogenate this sole alkene to give ring–$\mathrm{CH_2CO_2Et}$ at that <carbon>. Select the <diastereomer> with this substituent cis to the pre-existing protected hydroxyethyl side chain, so the newly installed ring H is cis to ring Me. Less hindered-face <hydrogenation> can assist this relationship, but the route should include separation/verification of the desired cis product rather than assert complete stereoselectivity without data.
Reduce the <ester> with <lithium aluminium hydride> to ring–$\mathrm{CH_2CH_2OH}$ and remove the TBS group from the other side chain. Both appendages are now two-carbon primary alcohols. Oxidize them to aldehydes under non-overoxidizing conditions, for example Dess–Martin oxidation, obtaining the cis dialdehyde with two ring–$\mathrm{CH_2CHO}$ groups. Treat with excess salt-controlled, nonstabilized ethylidenetriphenylphosphorane under conditions favouring kinetic Z <olefination>; isolate the \b[Z,Z product]. Each aldehyde <carbon> becomes the inner vinylic <carbon> of its crotyl group, while the <ylide> supplies $\mathrm{CHMe}$.
This order postpones both stereodefined alkenes until after <hydrogenation>, so they are not accidentally saturated. It also avoids assuming that a crotyl <grignard reagent> adds without allylic transposition or that direct <alcohol> deoxygenation fixes the required ring stereochemistry. An achiral synthesis gives a <racemic mixture> pair with the specified relative configuration.
\Image[/past-exam-of-the-chemistry-course-of-the-year-3-of-the-natural-sciences-course-of-the-university-of-cambridge/2022/paper-1-q11-second-route.png]
{title=Original stereochemical plan through a cis diol/dialdehyde and late double Z-selective Wittig olefination}
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