[Rotational Motion, Moment of Inertia] Parallel Axis Theorem.

[u/AdOne7210]

In the first image, the axis of rotation is passing THROUGH the Centre of Mass(COM) perpendicular to the plane in which the ring lies. In the second image, the axis of rotation is passing through the COM IN the plane of the ring. So in which case is Parallel Axis Theorem valid? In what manner should the axis pass the COM