While logged into the email account that manages your Google profile, go to Google search and type “my business” in the search bar, or click this url:

https://www.google.com/search?q=my+business

This should bring up your listing information. If you have multiple profiles connected to the same email, you will need to choose the profile you want to find the Business ID number for. Click View Profile.

You should see a screen that looks like this.