= Solution
Let $\mathrm{Ar}=p\!-\!\mathrm{MeOC_6H_4}$. One standard route is:
$$
\mathrm{ArBr}
\xrightarrow[\text{dry ether or THF}]{Mg}\mathrm{ArMgBr}
\xrightarrow[\text{then aqueous workup}]{CH_3CHO}
\mathrm{ArCH(OH)CH_3}
\xrightarrow[\Delta]{\text{catalytic }p\text{-TsOH}}
\mathrm{ArCH{=}CH_2}
\xrightarrow{mCPBA}\mathrm{ArCH{-}CH_2}
$$
where the last two <carbons> are joined through <oxygen> to form the \b[<epoxide>] shown in the product drawing.
\Image[/past-exam-of-the-chemistry-course-of-the-year-1-of-the-natural-sciences-course-of-the-university-of-cambridge/2021/paper-1-q3-synthetic-route.png]
{title=Grignard addition, dehydration and epoxidation furnish the methoxy-substituted styrene oxide}
Use rigorously dry conditions for Grignard formation/addition; quench only after the <aldehyde> addition. <Dehydration> gives the styrene, and peracid <oxidation> transfers <oxygen> across its double bond. The methoxy substituent is compatible with this sequence. No asymmetric reagent is specified, so the target <epoxide> is racemic.
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