First we will determine which of the two chair conformers of $cis- 1, 4$ - dimethylcyclohexane is more stable. One chair conformer has one methyl group  in an equatorial position and one methyl group in an axial position. The  other chair conformer also has one methyl group in an equatorial position and  one methyl group in an axial position. Therefore, both chair conformers are  equally stable.