Honorific noun used to politely refer to the trouble or effort one causes someone else. Often used in set phrases like お手数ですが (I'm sorry to trouble you, but...) or お手数をおかけします (I apologize for the inconvenience).
See also: 手数
I'm sorry to trouble you, but could you send the email once more?
お手数をおかけして申し訳ございません。
I apologize for causing you trouble.
I called several times and ended up putting the teacher to some trouble.
I'm very sorry for the trouble, but could you please check the documents?
I'm sorry to keep troubling you, but I appreciate your help.
迷惑 carries a stronger negative sense of nuisance or annoyance, whereas お手数 is a softer, more polite way to refer to inconvenience caused to someone.
手数 is the plain word for trouble or effort, while お手数 adds the honorific お to politely acknowledge the trouble caused to someone else.
Standard polite spelling; the honorific prefix お is written in kana.
Honorific prefix お + 手数 (てすう, 'trouble, effort'). The reading おてかず is a less common variant.