The negative sign on the acceleration is only a vector quantity that means the object is accelerating to the left. Hence, we can only focus on it magnitude which is 4 m/s^2. Acceleration is the change in velocity over time. The change in velocity must be 24 m/s - 0 m/s, if you want the object to stop. Therefore,
a = (v2 - v1)/t
4 = (24 - 0)t
t = 6 seconds
The object will stop after 6 seconds.
