trans-1-Bromo-2-methylcyclohexane is heated with $\mathrm{NaOEt}$ in ethanol. The major alkene is:

The stable chair has Br and $\mathrm{CH}{}_3$ both equatorial. E2 needs the diaxial conformer, where $\mathrm{CH}{}_3$ on C2 is axial, so the C2-H is equatorial and not anti to Br. Only the axial H on C6 is anti-periplanar, giving the double bond C1=C6, i.e. 3-methylcyclohexene, despite its lower substitution.