Century Link Modem 4000

You will need:

(1) Ethernet to Thunderbolt adaptor Thunderbolt to Gigabit Ethernet Adapter - Apple

(2) Ethernet Cat-6 or higher (Cat-7, Cat-8 etc.) cable

Connect one end of ethernet cable to one of the LAN ports (there may be three or four of these LAN ports, they are often colored a distinctly different color than the single WAN port; they are also labeled "ethernet") on the Century 4000 Link modem. Connect the other end of the ethernet cable to the adaptor, and the other end of the adaptor connects to one of your Thunderbolt ports on the Mac mini.

Open Network Preferences, it should show the ethernet connection.

Here are the instructions for connecting to a Centurylink Modem 4000

https://www.centurylink.com/home/help/internet/modems-and-routers/greenwave-c4000.html