Why did CBS televise yesterday's Panther-Falcon game? Being an NFC game, shouldn't that have been a Fox broadcast?

I don't know the exact equation but when CBS won the deal to network broadcast the first eight weeks of Thursday Night Football it meant they would be televising games involving NFC teams playing road games, which were previously Fox's domain. So a deal was also made to allow Fox and CBS to occasionally switch games that each network would have normally shown to allow Fox to show AFC teams playing on the road (normally CBS's property).

But again, I don't know what kind of formula/agreement they used to decide which network got which games.

because Fox had 3 game and if they had the game that would be 4. CBS had 1 game and that was a really bad game so with that game they would have 2

4-1 or 3-2

In most markets, CBS and FOX are one and the same when it comes to the NFL.

Plus the old traditional CBS does only NFC games and NBC does only AFC games is gone.

They have doing that all year long.