I've been working on this problem for a few days, but I haven't been able to find $x$ algebraically. (Maybe I'm missing something obvious?)
$2^x (6 - x) = 8x$
Using a MATLAB program, I found the solutions $ x = 2, 3, 4 $.
I tried using Wolfram|Alpha, but since it didn't provide steps, I assume it solved the equation numerically too. Which is not very elegant.
Follow up: I guess the problem I was looking at was not well written, and should have asked for integer solution.