Given the formula:

the bond between which two atoms has the greatest degree of polarity?
a. c and c
b. c and o
c. h and c
d. h and o

I would say D because oxygen is a highly electronegative atom and the OH b bonding is known to have high levels of polarity for example H-O-H in water.  This is why alcohols are miscible in water eventhough they are mostly non-polar.

The CH bond is more likely to be non-polar as it is with alot of hydrocarbons.  

For cyclohexane compounds drawn in a chair conformation:   -axial bonds are vertical  -equatorial bonds are parallel to two bonds within the ring.  thus, as i assume the chair conformation is drawn:   -the x group is in an axial position, as are the five other vertical bonds.  -three axial bonds are on the top face of the ring  -the other three axial bonds are on the bottom face  the position of the second substituent on each ring carbon is equatorial.  gauche groups must be on an adjacent carbon such as carbon 6 and carbon 2, and also gauche groups are rotated by 60 degrees relative to each other.  drawing the newman projections for c1–c2 and c1–c6 aids in visualizing the groups that are gauche to the y group on c1.  click this link and watch some academic videos that may you more understand the topic