Minimum of Absolute Value

The inequality $x^2 \le 6|x|$ is satisfied for all $[-6,0] \cup[0,6].$ If $b \le x \le 0$ is a sufficient condition and $x \le a$ be a necessary condition, then we require $a = 0, b = -6 \Rightarrow |a-b| = \boxed{6}.$