Answer
It takes 0.0625 seconds.
Work Step by Step
We can find the period of the motion.
$T = \frac{1}{f} = \frac{1}{4.00~Hz} = 0.250~s$
If the object moves from x = 0 to x = -1.80 cm, the object completes one-fourth of a cycle. We can find the time this takes.
$t = \frac{T}{4} = \frac{0.250~s}{4} = 0.0625~s$
