after the infant's push, but before the box came to a stop, the box accelerated at a rate of 2 m/s^2. what was the coefficient of kinetic friction between the box and the floor during its motion?

Is that an accleration rate or a deceleration rate? Is the ground level?

If level and decelerating, then

a = F/M = muk*M*g/M = muk*g

muk = a/g = 0.2 is the coefficient of kinetic friction