be engaged in的意思是“使从事于”、“使忙于”，它的同义词组是be busy with。例如：

We should all be engaged in good causes. 我们都应从事好的事业。

They are engaged in the study of music.他们在从事音乐研究。

He is busy with his homework. 他在忙着做作业。

By the end of this month we will be busy with company's salary report. 这个月的月底我们又将忙于做出公司职工的工资报表。