Answer
The angular speed is zero at time $~~t=12~s$
Work Step by Step
Since the initial angular momentum is positive, the applied torque must be negative since it reverses the rotation.
We can find the required time $t$ for the torque to change the angular momentum to $0$:
$\tau~t = \Delta L$
$t = \frac{\Delta L}{\tau}$
$t = \frac{-600~kg~m^2/s}{-50~N\cdot m}$
$t = 12~s$
The angular momentum is zero, and thus the angular speed is zero, at time $~~t=12~s$
