busydoing（忙於做某事）,永遠都是固定搭配，我們英語老師說的，busytodo是語法錯誤。這個一般用於現在進行時

Busy後面跟doing。Busy是形容詞，它組成的短語用法有be doing something 表示忙於做某事相當於be busy with something。它的名詞是business，表示的意思是生意，商業，事務。如，He will go to Beijing on business for three days.他要去北京出差三天。

It's none of your business.不管你的事兒。

He wants to do business when he grows up.他長大想做生意。

be busy with sth

例句 I am busy with my homework.

例句 She is busy washing her hands.