Final answer:
In a cyclohexane ring, an E2 reaction will not occur if the leaving group and the hydrogen are not anti-periplanar.
Step-by-step explanation:
The cyclohexane ring will not undergo an E2 reaction if the leaving group (lg) and the hydrogen are not anti-periplanar. In other words, they should not be in the same plane and aligned in the opposite directions. In a chair conformation of cyclohexane, an lg and a hydrogen atom are considered anti-periplanar if they are on opposite sides of the ring and in the same plane. If they are not anti-periplanar, then an E2 reaction will not occur.
For example, let's consider trans-1,2-dimethylcyclopropane. In this molecule, the methyl groups are not anti-periplanar to each other, so an E2 reaction will not occur.
Note that the conformation and position of substituents around the cyclohexane ring determine whether an E2 reaction can occur or not.