If you have a difficult situation on your hands, you have to deal with it.

If the police carry on like this they'll have a riot on their hands. 如果警方继续这样下去，那么他们将要面临一场暴乱。

She has a battle on her hands if she wants the organization to change. 如果她要让机构发生改变的话，那么她会有一场仗要打。

to be to blame for something

We have the blood of these people on our hands (= we are responsible for their death or injury). 我们要为这些人的伤亡负责。

His death is on the government's hands. 政府要为他的死负责。