Question

How many of the carbon–carbon bonds in the compound have staggered conformers that are all equally stable?

Answer 1

Answer : The 3 carbons which are bonded to $CH_{3}$ have equally stable staaggered conformers.

There are 3 identical atoms of hydrogens in 2-methylhexane molecule (refer attached figure)

Therefore any degree of rotation of 60 or 180 or 300 in C-C bond will give a stable conformer of the same energy.

The image is attached for the stable staggered conformation.

Answer 2

In stereoisomers, there are two classifications: staggered and eclipsed conformations. The staggered conformation is when the bonds are not symmetric. Eclipsed is less stable than the staggered conformation. It actually depends on the compound. For example, the ethane is drawn in the staggered conformation, which only has 1 C-C single bond.