I've gotten many questions about this from both students, and current existing course staff since type inference is a reasonably new age concept that is getting picked up in the programming languages of the 2010s and 2020s.
The lesson gives a pretty good starting point, especially the 7-minute walkthrough here on the basics of type inference.
I redid a few of the older problems using var
type inference across a few of the past homework problems to see this in action. I highly suggest checking these out.