Back when we published our Mario Kart 8 Deluxe preview, focused on the Battle Mode, we mentioned the presence of a LAN multiplayer option. It was notable because, while standard local wireless play supports eight players, LAN allows the full complement of 12 players that you normally get in online matches. We quipped that it would be good at events "if you successfully rig this up with those darn LAN adapters". Some pointed out, not without logic, that perhaps only one adapter would be needed to 'host' the others, however, making it an option more readily available to groups.
The reality seems to be that it is ultimately only really suitable for competitions and events; arguably that's to be expected. A press release for the game emphasizes the requirements to use the LAN mode, including the need for each console to have its own adapter.
Up to 12 consoles in TV mode can be connected via LAN Play***, with one or two players per connected Nintendo Switch for a maximum of 12 players
***For LAN Play each console requires its own USB to LAN adapter, sold separately. At least two connected Nintendo Switch consoles are required for LAN Play.
Specifying TV mode and a LAN adapter for each system naturally limits its usefulness outside of core events, though you could get a full complement of 12 racers at 60fps through six consoles using two-player splitscreen.
To be fair to Nintendo this is really a 'bonus' mode, not something to be used often. In fact, the LAN option isn't even visible as standard, you have to do some button presses for it to even appear:
From the main menu you need to hold L and R and then click the left stick to swap Wireless Mode to LAN Mode. You'll also need a router connected to the Internet in between the consoles (similarly to Splatoon on Wii U, it needs to 'authorise' online and then it runs a true LAN after that).
So there you have it. If you fancy some 12 player LAN gaming, start buying some LAN adapters. Or just play in standard local wireless or online, that might be less hassle.