Which statement best explains the role of a
catalyst in a chemical reaction?
(1) a catalyst is added as an additional reactant
and is consumed but not regenerated.
(2) a catalyst limits the amount of reactants used.
(3) a catalyst changes the kinds of products produced.
(4) a catalyst provides an alternate reaction pathway
that requires less activation energy.

The answer is (4). If you look at a Maxwell-Boltzmann energy curve, you will see that lowering the activation energy will increase the proportion of molecules with sufficient energy for a successful reaction collision. Therefore, a reaction with lower activation energy will proceed more quickly. Often, this lower activation energy is obtained by another mechanistic pathway. Catalysts increase reaction speed through these two basic mechanisms.

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