= Solution
Disconnect the new bond between the two six-carbon units. One portion of <bromocyclohexane> supplies a <grignard reagent>; another supplies <cyclohexene oxide>:
$$
\begin{aligned}
\mathrm{C_6H_{11}Br}&\xrightarrow{\mathrm{Mg,\ dry\ ether}}\mathrm{C_6H_{11}MgBr},\\
\mathrm{C_6H_{11}Br}&\xrightarrow{\mathrm{base,\ heat}}\mathrm{cyclohexene}\xrightarrow{\mathrm{peracid}}\mathrm{cyclohexene\ oxide}.
\end{aligned}
$$
A bulky strong base can favour <E2 elimination> in the alkene-forming step; a peracid such as <meta-chloroperoxybenzoic acid> provides <epoxidation>. None of its carbons enters the target.
Treat <cyclohexene oxide> with <cyclohexylmagnesium bromide>, then perform acidic aqueous work-up. Backside attack on one <epoxide> <carbon> breaks its C–O bond and installs cyclohexyl opposite the retained <oxygen>. Protonation of the <oxygen> gives \b[trans-2-cyclohexylcyclohexan-1-ol], the required relative configuration. The two six-carbon reactant portions supply all 12 target carbons. An achiral synthesis produces a <racemic mixture> trans pair; obtaining only the particular <enantiomer> represented by the drawing would require resolution or an enantioselective step. The useful stable chair can place the two large trans-1,2 substituents approximately diequatorial.
\Image[/past-exam-of-the-chemistry-course-of-the-year-1-of-the-natural-sciences-course-of-the-university-of-cambridge/2022/paper-1-trans-cyclohexanol-synthesis.png]
{title=Original two-branch synthesis from bromocyclohexane and anti epoxide opening to the trans alcohol}
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