Answer
The braking torque would have to be applied for a time of $1.6~seconds$
Work Step by Step
The angular impulse is equal to the change in angular momentum. We can use the change in angular momentum to find the time that the torque should be applied:
$\tau~t = \Delta L$
$t = \frac{L_f-L_0}{\tau}$
$t = \frac{0-6.40~kg~m^2/s}{-4.00~N \cdot m}$
$t = 1.6~s$
The braking torque would have to be applied for a time of $1.6~seconds$.
