Once you add an annual night limit to a listing, you'll be able to see the number of booked nights for the current year, out of the total annual nights, in the Multi-Calendar's listings tab (on the left side of the Multi-Calendar).
For example, in the image below, a listing ("3 Floor House") has an annual night limit of 30 nights and has 0 booked nights so far ("0/30").
Tip:
You can also create a custom report for listings, and add specific columns to view the annual nights limit.