If you wish then skip ahead to the in summery part of this post.
If I understand this correctly then the nuber of games in a league should be three times:
Where g is the number of games that will occur and t is the number of teams in the league. I'm much better at algorythms so I will write one of those as well.
According to Wolfram Alpha:
games = 0
for p = 1 to teams
games += p
games *= 3
For example if we have 4 teams then , therefore .
In our case all this must occur three times so:
You play 6 matches per day and there are 365 days in a year therefore you could have 38 teams per yearly league so there is no trouble with 9 time wise. However there are other problems with your set-up.
You need an odd number of teams to satisfy having teams play there matches in sets of 2.
You need a number of teams that gives an integer when divided by 4 to satisfy playing games in daily rounds of 6.
games that will be played =
The first two conditions wont ever be true together.
3 teams creates 9 games, thats 2 per team. Exactly 6 games per round (not ok), teams play exactly 2 games per playing week (ok).
4 teams creates 18 games, thats 9 games per team. Exactly 6 games per round (ok), teams play exactly 2 games per playing week (not ok).