From Longman Dictionary of Contemporary Englishhave something/somebody on your handshave something/somebody on your handsDEAL WITHto have a difficult job, problem, situation etc to deal with I’m afraid we have a murder on our hands, Inspector. → hand
Examples from the Corpus
have something/somebody on your hands• The Khedive is starting to realize that he might have trouble on his hands.• It is still instinctively held that those involved in engineering science should be useful handymen and will have oil on their hands.• They submitted lest they kill him; his death from the fast would have been on their hands. 