We are given the equation $\frac{2}{3}(x-2) = 2x - 8$ and asked to solve for $x$.

1. Problem Description

We are given the equation $\frac{2}{3}(x-2) = 2x - 8$ and asked to solve for $x$.

2. Solution Steps

First, distribute the $\frac{2}{3}$ on the left side of the equation:

$\frac{2}{3}x - \frac{4}{3} = 2x - 8$

Next, multiply both sides of the equation by 3 to eliminate the fractions:

$3(\frac{2}{3}x - \frac{4}{3}) = 3(2x - 8)$

$2x - 4 = 6x - 24$

Now, subtract $2x$ from both sides of the equation:

$2x - 4 - 2x = 6x - 24 - 2x$

$-4 = 4x - 24$

Add 24 to both sides of the equation:

$-4 + 24 = 4x - 24 + 24$

$20 = 4x$

Finally, divide both sides by 4 to solve for $x$:

$\frac{20}{4} = \frac{4x}{4}$

$5 = x$

3. Final Answer

$x = 5$