Just to make things clear, a Host is the device with the Steam executable, where the games are actually running, normally a PC; a Client is the device from which you are watching the stream.
Usually, to connect from a Host to a Client, on the Clients' screen, there will be a code (the one you mentioned). You have to insert that code on the Host Device, under this menu: Steam > Settings > Remote Play > Pair Steam Link.

host use steam desktop app and plays the game locally
client, can use steam app, or steam link apps

when pairing steam link to host pc, the link app will give a pairing code (#####)
on host, steam -> settings -> remote play -> pair link -> enter code -> (#####)

if the client is asking for a code, you need to enter the code set on the host
on host, steam -> settings -> remote play -> pair link -> set pin -> (4-10 digits)