B is correct.
The point of this question is to check if the concept of the inflection point is understood; the given function will have one inflection point, but also points where the second derivative is zero but is not an inflection point.
Here $f^{\prime}(x)=\frac{x^4}{4}-2 x^3+3$ and $f^{\prime \prime}(x)=x^2(x-6)$, so $f^{\prime \prime}(x)$ vanishes at $0$ and $6;$ but only $6$ is an inflection point since $f^{\prime \prime \prime}(0)=0$ while $f^{\prime \prime \prime}(6) \neq 0$.
