\(v\left(t\right)=s'\left(t\right)=-\dfrac{3}{2}t^2+12t\)
\(v'\left(t\right)=-3t+12=0\Rightarrow t=4\)
\(v\left(0\right)=0\) ; \(v\left(4\right)=24\) ; \(v\left(6\right)=18\)
\(\Rightarrow\max\limits_{t\in\left[0;6\right]}v\left(t\right)=v\left(4\right)=24\) (m/s)