We can first look at how many games are played in a SINGLE nine-team round-robin (each team playe each other once) and then multiply our answer by 2 at the end

Each team must play 8 games. So, 9 teams, 8 games each. To find the total number of games to be played, we must multiply 9 by 8 and divide by two (We must divide by two because otherwise we count, say Team A playing Team B as a different game than Team B playing Team A (when in reality they are both the same game) and for every possible combination there is a similar duplication)

So, if each team played each other ONCE, there would be a total of 72/2 = 36 games

If each team played each other TWO times, there is a total of 36*2 = 72 games

there will be 72 games scheduled.