Answer
No solution
Work Step by Step
$\frac{2}{3} *(x - 4) = \frac{1}{3} *(2x - 6)$
$\frac{2x}{3} -\frac{8}{3} = \frac{2x}{3} - \frac{6}{3}$
$\frac{2x}{3} -\frac{8}{3} (+\frac{2x}{3})= \frac{2x}{3} - \frac{6}{3} (+\frac{2x}{3})$
$\frac{-8}{3} = \frac{6}{3}$
This last statement is false, thus, there is no solution.