On One's Hands Meaning

(idiomatic) Being one's liability or responsibility; with which one is lumbered.

Example: 1986, Romain Gary, Ralph Manheim, The life before us
  When I started yelling, the other kids started yelling, so Madame Rosa had seven kids on her hands, all bellowing for their mothers...
1990, Kazuo Ishiguro, The remains of the day
  It is most curious to see that you have so much time on your hands that you are able to simply wander about this house bothering others...