busy doing和busy to do的含义不同、用法不同。be busy doing sth其实也可以是be busy (in) doing sth.意为忙于做某事；be busy to do sth.一般是be too busy to do sth.意为太忙了以至于不能干什么。

People are always out in their cars,watching television or busy doing something else.

人们总是驾车外出，或者看电视，再不就是忙点其他什么事情。

I am busy doing my homework right now.

我现在正忙着在做课外作业。

Was it because you were too busy doing everything else?

是因为你有很多别的事情要忙着做吗？做了很多事，意味着你很忙。

Because I was busy doing something else.

我在处理别的事。

I'm busy doing that today.

我今天在忙着做那件事情。