Running a Hex would mean 5 rounds instead of 4. The Crenshaw-Berger pairing tables in the rulebook can be used to generate pairings, showing which players have white and which have black.
The challenge with 6 players and 4 rounds is that you might wind up with pairing a 3.0 against a 1.0 or lower score to avoid pairing someone against the same player twice. It’s also possible to box yourself in for the last round.
This is the sort of thing you can practice by hand using 3x5 pieces of paper and just randomly assigning results to a round then seeing how that affects pairing subsequent rounds. You can do it with a pairing program like WinTD or SwissSys, too, but I think it is very instructive for a new TD to do some pairings by hand so they know when not to just use the computer’s pairings.
This has come up in the forums a few times, here’s one thread that discusses it: