be busy (with something) 忙（于某事）
be occupied 被占用了，没时间
I am occupied.
我很忙。

work one's butt off 工作很忙，很努力卖命地工作
Hey, let us go out clubbing.
嘿，一起出去嗨一嗨吧。
I'm working my butt off.
我工作都快忙死了。

be tied up 忙得不可开交的，不得闲地
Hey, I cannot go out today because I am tied up with work.
嘿，我今天不能出去，我工作超级忙。

a million things 很多很多事情
Hey, I cannot go out today I have like a million things to do.
嘿，我今天不能出去了，我有巨多的事情要做。

to be piled up 堆叠，堆积（成山）
My work keeps on piling up without an end… so I do not think I will make it today!
我的工作越堆越多都没完了...我猜我今天应该是去不了了。

be booked 被预定，被占用，没空
Hey, I am sorry but I am all booked today. Can I have a raincheck?
嘿，不好意思我今天时间都排满了。我们能改天吗？

be in the middle of something 正忙于某事
当你在忙碌时接到电话
Hey, do you have a minute?
嘿你有时间吗？
Hey, I am sorry… I am kind of in the middle of something. I will call you back in a bit.
嘿不好意思，我现在有一点点忙。我待会儿给你回电话。

no time to catch one's breath 连喘口气的机会都没有
当你和一个人约好见面，你迟到了，对方就会说
Hey, finally you are here! Care to explain yourself?
嘿，你终于来啦！要不要解释一下？
Hey, sorry I didn't even have time to catch my breath... Give me a second.
嘿，不好意思，我连喘口气的机会都没有，等我一下啊。

on the go 忙个不停，忙得不可开交
let's go out! Come on... It has been a while!
出去嗨吧！拜托... 好久都没出去玩了！
I am sorry but my new work always keeps me on the go!
不好意思！我的新工作真的太忙了！