 Solution

Both side chains have the order ring–$\mathrm{C}{\mathrm{H}}_2\mathrm{CH}=\mathrm{CHMe}$, 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 ring–$\mathrm{C}{\mathrm{H}}_2\mathrm{CHO}$ substituents, which can undergo two Z-selective ethylidene Wittig reactions.

Use the starting 2-methylcyclohex-2-en-1-one in a reductive alpha-alkylation. Conjugate reduction under dissolving-metal/enolate-trapping conditions, followed by a primary electrophile $\mathrm{BrC}{\mathrm{H}}_2\mathrm{C}{\mathrm{H}}_2\mathrm{OTBS}$, 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:Hydrogenate this sole alkene to give ring–$\mathrm{C}{\mathrm{H}}_2\mathrm{C}{\mathrm{O}}_2\mathrm{Et}$ 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–$\mathrm{C}{\mathrm{H}}_2\mathrm{C}{\mathrm{H}}_2\mathrm{OH}$ 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–$\mathrm{C}{\mathrm{H}}_2\mathrm{CHO}$ groups. Treat with excess salt-controlled, nonstabilized ethylidenetriphenylphosphorane under conditions favouring kinetic Z olefination; isolate the 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.