= Solution
\b[The first transformation is two successive dehydrohalogenations; the second opens the lactone by two methyl additions and then closes a six-membered cyclic ether.] Both schemes must be accounted for within this part.
For the dichloride, write $R=\mathrm{cyclohexyl}$. In the product-forming path, <tert-butoxide> removes a hydrogen from the methyl group of $\mathrm{R-CCl_2-CH_3}$. Draw arrows from the base lone pair to H, from C–H into the C–C bond, and from C–Cl to Cl. This <E2 elimination> gives $\mathrm{R-C(Cl)=CH_2}$. A second base-induced elimination removes a vinyl hydrogen and the remaining chloride, forming $\mathrm{R-C\equiv CH}$. The second elimination is more demanding because a vinylic bond is involved, consistent with the strong-base, heated conditions. This route explains the displayed product without asserting that no other elimination regioisomer can ever form.
For the lactone, a methyl equivalent from <methylmagnesium iodide> attacks the ester carbonyl carbon, with its pi pair moving to oxygen. Collapse of the tetrahedral intermediate reforms C=O and cleaves the acyl–oxygen bond, opening the ring to the magnesium alkoxide corresponding to $\mathrm{HO(CH_2)_4C(=O)CH_3}$. The newly formed <ketone> is more susceptible to a second methyl addition; its pi pair again moves to oxygen. After water workup, the product is the diol $\mathrm{HO(CH_2)_4C(OH)(CH_3)_2}$.
Under acid and heat, protonate its tertiary OH, then move the C–O pair onto oxygen as water leaves. The resulting $\mathrm{HO(CH_2)_4C^+(CH_3)_2}$ is trapped intramolecularly by the remaining primary-alcohol oxygen. Its lone pair forms the closing O–C bond, producing a six-membered cyclic oxonium ion. Deprotonation yields \b[2,2-dimethyloxane], also called 2,2-dimethyltetrahydropyran. Ring closure retains four chain methylenes; it does not form a five-membered ring. The two methyl groups both derive from the two equivalents of Grignard reagent.
\Image[/past-exam-of-the-chemistry-course-of-the-year-1-of-the-natural-sciences-course-of-the-university-of-cambridge/2024/paper-1-organic-mechanisms.png]
{title=Original electron-flow schemes for double elimination, lactone addition and acid-induced ether formation}
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