It's an interesting question, but as with most hypotheticals, it poses some problems - namely that, well, secession did happen, at least in this universe. So, in order to answer this question in the way your teacher is probably looking for, we must be imaginative and creative with what we already know.
Start with this:
1) Try to determine what you think are the 2-3 main reasons that the South separated from the Union.
2) Imagine what would have needed to be different in order for these reasons to be invalidated. Not "no slavery" because that doesn't show your understanding of the social, political, geographical, and cultural mechanisms that created and enabled a slave economy. Instead, think along the lines of "easing the Southern economy's entrenched reliance on agriculture so that slavery became unnecessary to those who saw it as an issue of profit"; etc. ( Of course, we now rightfully see slavery as a moral issue, but rich plantation owners in the South who supported secession most certainly did not.)
Hope this helps you get started!