An merry-go-round is an example of circular motion.
The angular momentum in a circular motion is calculated as the product of the moment of inertia times the angular speed.
It is analogous the the linear moment, which is the product of the mass times the speed, but in the circular motion you use the moment of inertia (instead of the mass) and the angular speed (instead of the linear speed).
The moment of inertia is identified by I and the angular moment by w.
Then, angular momentum, L = I * w.
Using hypotethical data I = 200 kg * m^2 and w = 1.51 rad / s (data taken from similar problem), you get:
L = 200 kg*m^2 * 1.51 rad/s = 302 N*m*s <----- answer
