What does "hand" mean in this context? Does it refer to a plan or a trick?

Native speaker’s answer
Rebecca
They're referring to the Professors' physical "hand" in this context. Buttercup and the Professor have swapped bodies! So, Buttercup in the Professors body is telling the Professor that his hand doesn't work and she can't pick up the phone. Ex: I slept for so long my eyes aren't open yet. Ex: My fingers are too sore to type on my phone.