Call the number of teams is n

We have: The number of games is n(n+1) games

But each game repeated 2 times 

So the number of the games is \(\dfrac{n\left(n+1\right)}{2}\)

There are 21 games

So \(\dfrac{n\left(n+1\right)}{2}=21\Rightarrow n\left(n+1\right)=42\Rightarrow n=6\)