To simplify this expression, we need to distribute the negative sign in the numerator and then combine like terms:

(x-4)-(x+2)/(x-2)
= x - 4 - x - 2 / (x - 2)
= (x - x) - (4 + 2) / (x - 2)
= -6 / (x - 2)

Therefore, the simplified expression is -6 / (x - 2).