[Schweitzer]

To restate, when combining moments of inertia you need to add the seperate moments of inertia and account for the displacement from the rotation axis.

I= I(disk) + I(child) + m(child)*r^2

where r is the displacement of the child from the axis it is rotating around.
(In this problem it asks to ignore the size of the child, thus you assume the child is a point particle with no moment of inertia so you only need the displacement term)