#### Answer

$y' = 24x^{2} - 16x^{3} +6 -6x$
$y'' = 48x - 48x^{2} -6$
$y''' = 48- 96x$
$y'''' = -96$
$y''''' = 0$
(and all higher derivatives will also be 0)

#### Work Step by Step

$y = (4x^{2}+3)(2-x)x$
$y = (4x^{2}+3)(2x - x^{2})$
$y = 8x^{3} - 4x^{4}+6x -3x^{2}$
$y' = 24x^{2} - 16x^{3} +6 -6x$
$y'' = 48x - 48x^{2} -6$
$y''' = 48- 96x$
$y'''' = -96$
$y''''' = 0$
(and all higher derivatives will also be 0)