The vampires won 12 games.
This is basically a system of equations problem. If we use the letter W to represent the number of wins, and the letter L to represent losses, the info we're given is below:
They played 20 games, so their wins and losses must add to 20.
They won 4 more than they lost.
Since we know that
They lost 8 games, which means they won 12 (just adding 4).