be engaged with的用法介绍如下：
be engaged with 与…洽谈,和…交战;忙于…
用法例句
I'll be engaged with a client this evening.
我晚上和一个客户有事。
I will be engaged with my boyfriend next week in his hometown Nanjing, and come back around one week.
我下个星期要和我男朋友去他的老家南京订婚，大约一个星期回来。
Anyone studying China with any social science must sooner or later be engaged with the fact that he has also to be a historian.
任何人用任何社会科学来研究中国或早或迟得面对一个事实，即他也得是一个历史学家。
Besides, the other end of the belt body is provided with a toothed hole which can be engaged with a thread part of the bolt body.
又，该带体的另一端则形成有齿孔，能于螺栓体的螺纹部咬合。
You are still faced with the position of the NORTH NODE in Capricorn and most likely this week your mind is likely to be engaged with some serious contemplations.
北交点仍在摩羯座，本周你的头脑可能一直认真盘算着什么。