The question asks us to determine the order of stability for different conformations of cyclohexane. Cyclohexane has several conformations, but the most common ones are the chair, boat, and twisted boat. Let's examine the stability of each:

1. Chair Conformation (Structure I): This is the most stable conformation of cyclohexane because it has the least amount of torsional strain and steric hindrance. All carbon-carbon bonds are staggered, leading to minimal strain.
2. Twist-Boat Conformation (Structure III): This conformation is more stable than the boat conformation due to reduced steric strain and torsional strain compared to the boat conformation, but it is less stable than the chair conformation.
3. Boat Conformation (Structure II): This is less stable than the twist-boat and chair conformations. It has more torsional strain because the carbon-carbon bonds are eclipsed, and there's steric strain due to flagpole interactions.

Based on the above analysis, the correct order of stability is:

This reflects the given correct answer.

Conclusion: The chair conformation is the most stable, followed by the twist-boat, and finally the boat conformation is the least stable.