What is the most stable conformer for 3,3-dimethylhexane, viewed along the #C_3-C_4# bond using Newman projections?

The most stable conformer for 3,3-dimethylhexane viewed along the #C_3-C_4# bond will have two ethyl groups in anti position and gauche interactions between two methyl groups and one ethyl group.

Start by drawing the bond line notation for the compound

Notice that you have one ethyl group and two methyl groups attached to #C_3#, and two hydrogens and one ethyl group attached to #C_4#.

Start by using a Newman projection template to draw the first staggered projection

Projection 1

Now rotate the front carbon by #"120"^@# to generate the other two staggered Newman projections

Projection 2 and Projection 3

Projection 2 and projection 3 will be less stable than projection 1 because in both cases you have gauche interactions between two bulky ethyl groups and a methyl group.

By comparison, projection 1 has the two ethyl groups in anti position, the repulsion between two methyl groups and one ethyl group being a little less unstable than the repulsion the other two staggered conformers have.

Therefore, projection 1 describes the most stable conformer for 3,3-dimethylhexane viewed along the #C_3-C_4# bond.