i want to run my 6400 directly from the internet not wi-fi . i have a modem and router which do i co

Don,

Your cable modem must connect only to your router. Then, your computer and the 6400 will plug into Ethernet ports on the router. Most routers only have 4 or so ports, often not nearly enough for a modern ham shack. To expand the available ports, you can buy inexpensive Ethernet switches from Amazon or other sources. They are available in 5, 8, 16 and even more ports. An "un-managed" switch will be fine.

73, Craig KØCF