The particle is moving such that its position is given by S(t) = t^3 - 6t^2 + 2.
When the particle changes direction the velocity changes sign.
Velocity is given by V(t) = S'(t) = 3t^2 - 12t
3t^2 - 12t = 0
=> 3t = 12
=> t = 12/3
=> t = 4
Before t = 4, the velocity of the particle is negative, after t = 4 the velocity of the particle becomes positive.
At t = 4, the particle changes direction.