One of the two chair structures of cis-1-chloro-3- methylcyclohexane is more stable than the other by 3.7 kcal/mol. Which is it?
Start with the wedge-dash notation for cis-1-chloro-3-methylcyclohexane, which looks like this
Since the compound is cis, the chloro and the methyl groups must either be on a wedge, or on a dash. The above image shows both of them on wedges. The first chair conformation for the compound looks like this
When performing a chair flip, the groups do not change orientation - UP will remain UP and DOWN will remain DOWN; however, what will change is their positions - axial positions will become equatorial and vice versa.
Notice that the chloro group was UP in axial position in the first chair, and is UP in the equatorial position in the second chair. The same is true for the methyl group, since it went from being UP in an axial position to being UP in the equatorial position.
When comparing the stability of chair conformers, always keep in mind that substituents "prefer" to be in the equatorial position, rather than in the axial position.
This is because groups bonded in axial positions will encounter unfavorable interactions will other groups bonded in axial positions on the same side. This unfavorable interaction, which is called 1,3-diaxial interaction, leads to steric strain (or steric hinderance), and significantly reduces the stability of the chair conformation.
If you compare the two chair conformations shown above, one has the chloro and methyl groups in axial positions, while the other one has them in equatorial positions.
This means that the second chair, in this example the flipped chair, will be more stable than the first.