$x^2 - 2x + 3 = 11$ OR $x^2 -2x+3 = -11$
$($Any one of them can be correct because of $\text{mod})$
Lets take first one:
$x^2 - 2x + 3 = 11$
$\implies x^2 - 2x - 8 = 0$
$\implies (x-4) (x+2) =0$
$\implies x= 4 \text{ or } x = -2.$
Now put these values of $x$ in the given equation $\mid -x^3+x^2 -x\mid $
for $x= 4,$ we will get $\mid 64+16-4\mid \quad= 52.$
for $x = -2,$ we will get $\mid 8 + 4 + 2 \mid \quad= 14.$
So, answer is $D.$