\[ |x-6| = |x-4x| - |x^2-5x+6| \] \[ |x-4x| = |-3x| = 3|x| \] \[ x^2-5x+6 = (x-2)(x-3) \] \[ |x-6| = 3|x| - |(x-2)(x-3)| \] \[ |x-6| + |(x-2)(x-3)| = 3|x| \] Critical points are \(0,2,3,6\). For \(x \ge 6\) \[ |x-6| = x-6, \qquad |(x-2)(x-3)| = (x-2)(x-3) \] \[ x-6 + (x-2)(x-3) = 3x \] \[ x-6 + x^2-5x+6 = 3x \] \[ x^2 -4x = 3x \] \[ x^2 -7x = 0 \] \[ x(x-7)=0 \] \[ x=7 \] For \(3 \le x < 6\) \[ |x-6| = 6-x, \qquad |(x-2)(x-3)| = (x-2)(x-3) \] \[ 6-x + (x-2)(x-3) = 3x \] \[ 6-x + x^2-5x+6 = 3x \] \[ x^2 -6x +12 = 3x \] \[ x^2 -9x +12 = 0 \] \[ x = \frac{9 \pm \sqrt{33}}{2} \] \[ x = \frac{9-\sqrt{33}}{2} \] \[ \therefore x = 7,\; \frac{9-\sqrt{33}}{2} \] These values do not match the given options. \[ \boxed{\text{D. None of these}} \]