Commerce Version: 11.3
The count shown next to the Item DISCOUNT TYPE represent the total number of active and inactive discounts. How to find the count of Active Item Discounts?
I believe you sent an email via leanpub to me. So I will answer it here as well
Showing the Active Item Discounts is not something builtin. If you want to, you would have to implement it yourself. Note that if you upgrade to 12.10 it will be much easier to do (you can still do it at 11.3 or any version up to 12.9, it'll be just more works)