with
 

From a non-native exercise:

-Cynthia was told by the teacher to engage __ (a preposition here?) the language of this lengthy novel.

Could I use with? (does it make sense?)

Re: with
 

Yes - with. Toengage with something = study it, explore it, find out about it :

One of the learning activities involved students doing a role play of a television panel discussion to engage with the issue of corporate social responsibility.

To engage with someone = to communicate with someone

We need to engage with local communities
If you fail to engage with stakeholders, there's the possibility rthat...


With an action/event in is used: - to engage in something = to participate in or be involved in something:

The students weren't very engaged in the lesson.
In 1776 the American Army was engaged in the Revolutionary War against...
He was engaged in a discussion about

The use of engage with in your context sounds a bit pompous though. It's a bit formal.

Re: with
 

Excellent answer. Thank you.