The problem asks what is wrong with the name 3-ethyl-4,4,-dimethylhexane. Is ethyl supposed to be on carbon 4 and the two methyls on carbon 3? McMurry's text if there is a branch point occuring equidistant from both ends, begin counting from the end nearer the second branch point. In this case, both ends are still the same distance from the second branch point. Do I begin counting from the end closer to the higher branched carbon, the carbon with two methyls attached to it?

I think in this case you want the name where the numbers give the smallest sum. So, 3+3+4=10 (as in 4-ethyl-3,3-dimethylhexane), which is smaller than 4+4+3=11 (as in 3-ethyl-4,4-dimethylhexane).

On a slightly more pedantic note, you should also watch the number and placement of commas in the name. Rather than 4,4,-dimethyl it should be 4,4-dimethyl (or 3,3-dimethyl in your case).