This is not possible. If there are 6 byes per round, after 4 rounds it might be possible to arrange it so all 24 players have had one bye. Or more generally, there must be a multiple of 4 rounds to balance the byes and give everyone the same number of matches. I could attempt to make such a schedule for 8 or 12 rounds if that suits, or a 10 round schedule where players had either 7 or 8 matches each.
