Answer
$f^{'}(x)=3x^2-12x+12$
$f^{''}(x)=6x-12$
Point of inflection occurs at input $x=2$
Work Step by Step
$f(x)=x^3-6x^2+12x$
Taking derivative with respect to x
$f^{'}(x)=3x^2-12x+12$
Again,taking derivative with respect to x
$f^{''}(x)=6x-12$
Putting
$f^{''}(x)=6x-12=0$
$6x-12=0$
$6x=12$
$x=\frac{12}{6}=2$
At input $x=2$, there exist point of inflection