I hope I'm not putting you out.
put out意思很多，在口语中可以表示：“使不方便，打扰，给某人添麻烦”。因此，当美国人说"I hope I'm notputting you out."时，他/她要表达的意思就是:"I hopeI'm not bringing you any inconvenience."、"I hopeI'm not causing discomfort to you."、"I hope I'mnot bothering you."。
Terry: Don't worry. I will try my best to help youwith such a tough task.
Benjamin: I hope I'm not putting you out. Your hands are full right now.
①You are terribly busy now.
②Excuse me. But I have something important to inform you.
③It's so great for your help.
④Leave it to me. I can handle it all by myself.
1. inconvenience n. 麻烦，不便
We apologize for any inconvenience caused during the repairs.
The practical inconveniences of long hair are negligible.
2. discomfort n. 不便之处
Living in the suburbs you may suffer a little discomfort.
The homes were pushed outwards even at the cost of the discomfort of commuting.
3. terribly adv. 非常，极度地
We are terribly sorry for being late.
My son has suffered terribly. He has lost his best friend.