If you click the "Public Network" lettering, does it give you the option to set it as a home network, or perhaps enterprise network?
You can either click on the "Local Area Connection" link and select Details or open a command window and type ipconfig /all which will show us what addresses your system is using. You can check to see if the addresses are appropriate or attach a picture. If something is private, you can always use Paint to erase some of the pertinent data.
I you want to remove a network, you can click on the park bench and delete or merge them there.