Find the value

= x(x  - 2)(x - 4) + 4(x - 2)

Taking (x - 2) common in both the terms

=(x - 2){x(x - 4) + 4}

$=(x-2)\left\{x^{2}-4 x+4\right\}$

Now splitting the middle term of $x^{2}-4 x+4$

$=(x-2)\left\{x^{2}-2 x-2 x+4\right\}$

$=(x-2)\{x(x-2)-2(x-2)\}$

$=(x-2)\{(x-2)(x-2)\}$

$=(x-2)(x-2)(x-2)$

$=(x-2)^{3}$

$\therefore x(x-2)(x-4)+4 x-8=(x-2)^{3}$