For E2 eliminations, always identify $\beta$-hydrogens anti-periplanar to the leaving group.
If only one such hydrogen exists, the reaction forms a single alkene product.
Step 1: Reaction type identification.
The reagent NaOEt/EtOH is a strong base, which generally promotes dehydrohalogenation (E2 elimination) from alkyl halides, producing alkenes.
Step 2: Requirements for a single alkene product.
Formation of only one alkene product indicates a stereospecific and regioselective E2 elimination, likely from a halide with an anti-periplanar $\beta$-hydrogen arrangement leading to a single alkene geometry.
Step 3: Analyze possible substrates.
Among the given structures, the compound in **Option (A)** — 1-chloro-2,6-dimethylcyclohexane — has only one $\beta$-hydrogen that is anti-periplanar to the leaving group (Cl).
Hence, elimination leads to a single alkene, 1-isopropyl-3-methylcyclohexene.
Step 4: Other options.
In options (B), (C), and (D), multiple $\beta$-hydrogens exist, which would lead to a mixture of elimination products (more than one alkene), contradicting the problem statement.
Step 5: Conclusion.
Therefore, the structure of compound Q that yields a single alkene product is **Option (A)**.
