Fixing error 262147 (Ping 9999) in Steam Trine 2

Many people encounter a strange delay of 9999 when trying to play Trine 2 with friends via Steam, and error 262147 appears when trying to connect to a network or private game.
With great difficulty, but I still managed to figure out and fix the problem.
Now the connection takes place both in the game over a local network (on two or more home computers) and over the Internet.