"忙于做某事"用英语可以说成"be busy doing something"。
"Be"是动词"是"的意思，表示现在的状态。"busy"是形容词，表示"忙碌的"。"doing"是动名词，表示正在进行的动作。"something"是代词，表示"某事"。
例句：
I'm busy working on my project. (我正忙于我的项目)
She's busy studying for her exams. (她正忙于为她的考试复习)
They're busy preparing for the party. (他们正忙于为聚会做准备)
注意：这是一种常见的表达方式，还有其它方式表达忙于做某事，例如:
be swamped with sth（忙于做某事）
be occupied with sth (忙于做某事)
be engaged in sth (忙于做某事)
例句：
I'm swamped with work today. (我今天忙于工作)
He's occupied with his new job. (他忙于他的新工作)
They're engaged in a new project. (他们忙于一个新项目)