To simplify this expression, we need to first combine like terms.

(4/x - 4 + 1/(2-x))x + 4x + 4/3
= (4/x - 4) x + 1/(2-x) x + 4x + 4/3
= 4 - 4x + x/(2-x) + 4x + 4/3
= 4 - 4x + x/(2-x) + 4x + 4/3

Now, let's simplify further if possible:

= 4 - 4x + x/(2-x) + 4x + 4/3
= 4 + x/(2-x) + 4x - 4x + 4/3
= 4 + x/(2-x) + 4/3
= 4 + (3x + 2)/(3(2-x))

Therefore, the simplified expression is 4 + (3x + 2)/(3(2-x)).