To see what's going on, start by drawing the graphs of $\displaystyle y = | x - 2| $ and $\displaystyle y = x^2 - 9x + 9$ and look at where the two graphs intersect.
we have $\displaystyle -\big(2x^2-9x+9\big)\le x+2\le2x^2-9x+9.$
we have to inequalities, then solve the first and the second one, each one of them will give ya a set, intersect those sets and you'll get the solution.