An understanding of cyclohexane conformations is necessary for a full appreciation of the structure and properties of substituted six-membered rings. In the structure on the left, the carbon atoms are dark-gray numbered spheres. The axial bonds are red rods and the equatorial bonds are blue. As we count around the ring from carbon #1 to #6, the uppermost bond on each carbon changes from axial (carbon #1) to equatorial (carbon #2) and back. It is important to remember that the bonds on a given side of a chair ring-conformation always alternate in this fashion. Secondly, we must remember that axial bonded groups usually are sterically hindered to a greater degree than are equatorial groups. The structure on the right shows the axial bonds of the chair conformer occupied by red spheres. If you have any doubt about this fact, you should examine the case of equatorial and axial t-butyl groups, shown by clicking the buttons in the first row below the model structures. In the stick model it is clear that the axial t-butyl group is forced to severely bend away from the two axial hydrogens cis to it.
The middle three examples presented here represent the cis-trans stereoisomers of the dimethyl cyclohexanes. Because of the alternating nature of axial and equatorial bonds noted above, 1,2- and 1,4-cis-disubstituted compounds must have one substituent in an axial orientation. The 1,3-cis-isomer may have both substituents in favorable equatorial locations. In the case of the trans-isomers, this relationship is reversed. You should confirm these facts for yourself with the assistance of a set of molecular models, or by using the models given here. The last example shows a similar stereoisomerism associated with two fused cyclohexane rings (the rings have two carbon atoms in common). Both the cis and the trans ring-fusions permit the six-membered rings to adopt chair conformations. In the cis-isomer, however, one of the ring carbons of a given ring is always axially oriented on the other ring. Consequently, the trans-decalin system is thermodynamically more stable than its cis-isomer.