Three stereoselective syntheses and the physicochemical properties of trans,trans-5-(4-ethoxy-2,3-difluorophenyl)-2-(4-propylcyclohexyl)tetrahydropyran, which is an important liquid-crystal compound with a large negative dielectric anisotropy (Δε=-7.3), are described. The key step in the construction of the trans-2,5-disubstituted tetrahydropyran ring in the first approach involved a benzylic cation mediated intramolecular olefin cyclization of a 2-allyloxy-1-arylethanol derivative. The second method included the Et2 Zn-induced 1,2-aryl shift of a bromohydrin obtained from a hetero-Diels-Alder reaction, followed by stereoselective bromination. The third approach utilized the hetero-Diels-Alder reaction of trans-4-propylcyclohexanecarboxaldehyde and a 2-aryl-3-(trimethylsilyl)oxy-1,3-butadiene, followed by stereoselective protonation. From results obtained by using a quantum chemical calculation method, the reason why the target compound shows a large negative Δε value is discussed.