To solve this equation, we need to simplify and then isolate the variable x.

First, we distribute the -2/3 to both terms in the parentheses:
4.5x - 2/3 8x + 2/3 10 = 4 - 2x
4.5x - 16/3x + 20/3 = 4 - 2x

Next, combine like terms on both sides of the equation:
(4.5 - 16/3)x + 20/3 = 4 - 2x
(13.5/3 - 16/3)x + 20/3 = 12/3 - 6/3x
(-2.5)x + 20/3 = 6/3 - 6/3x
-2.5x + 20/3 = 2 - 2x

Now, we want to isolate the variable x. Let's get all the x terms on one side and the constant terms on the other side:
-2.5x + 2x = 2 - 20/3
-0.5x = 6/3 - 20/3
-0.5x = -14/3

Multiplying both sides by -2 gives:
x = 28/3

So, the solution to the equation is x = 28/3.