Answer
$t=4s$
Work Step by Step
When the velocity is zero then the maximum positive coordinate reached by particle occurs:
$v=24t-6t^2=0$
Taking $t$ common we obtain:
$t(24-6t)=0$
Thus, either $t=0 s$ or $24-6t=0$, which simplifies to $t=4s$
So, the particle reaches the maximum position at time $t=4s$
