The most stable isomer of 3-methoxycyclohexanol is (A). This is because it has the lowest energy. The other isomers (B, C, and D) have higher energies because they have more steric strain. Steric strain is caused by the repulsion of atoms or groups that are close together in space. In (B), the methoxy group is in the axial position, which puts it in close proximity to the hydrogen atoms on the adjacent carbon atoms. This causes steric strain, which makes (B) less stable than (A). In (C), the methoxy group is in the equatorial position, but it is still close to the hydrogen atoms on the adjacent carbon atoms. This also causes steric strain, which makes (C) less stable than (A). In (D), the methoxy group is in the axial position and it is also close to the hydroxyl group. This causes even more steric strain, which makes (D) the least stable isomer.
In conclusion, the most stable isomer of 3-methoxycyclohexanol is (A). This is because it has the lowest energy. The other isomers (B, C, and D) have higher energies because they have more steric strain.