Synthesis of (1S,2S,4S)-4-ethenyl-5-methylcyclohexane-1,2-diol
Because the target structure contains the motif of a cyclohexane-1,2-diol, I suggest an approach including a Diels-Alder reaction (DA in the illustration below) of 1,3-butadiene and the commercially available diethyl acetal of propargyl aldehyde:

The hydrolysis of the acetal then sets the stage to install the methyl group with the cuprate and 1,4-selectivity in respect to the carbonyl group.  As an intermediate protection of the aldehyde, a cyclic acetal is installed. The Prévost reaction typically yields 1,2-(trans)-diols, thus possibly here, too (brief review).  Eventually, the deprotected aldehyde is transformed into the exocyclic alkene with the Lombardo reagent. Contrasting to the conditions of a Wittig reaction, the conditions of the Takai-Lombardo reaction are milder (absence of a strong Bronsted base).
Alternative installations of the (trans)-diol could be achieved e.g., by epoxidation and subsequent ring opening with a peracid like mCPBA or (in situ generated by) oxone.