Spasms of the face and extremities with slowly waving hands and feet are symptomatic of:

Huntington's disease. This disease is an inherited dementia that affects the normal body movements, and causes lack of coordination; it may also affect some mental abilities and and some points of personality.
These symptoms such as the spasms of the face and extremities, and waving of the hands and feet are a result of the hypotonia and muscle weakness.

The answer is d. when it begins to fall back to the child's hand