Every character has an alignment. They're either Laughter (Yellow), Power (Red) or Knowledge (Green).
When you're fighting against a character of a different alignment, you either do more damage to them, or they do more damage to you.
i.e: Power(Red) characters do 1.5x damage to Knowledge(Green) characters
Knowledge(Green) characters do 1.5x damage to Laughter(Yellow) characters
Laughter(Yellow) characters do 1.5x damage to Power(Red) characters
So, for the opposing nature k.o, merely beat one of the enemies with a character who does 1.5x damage against them. This might mean changing your deck a bit as some characters only have one alignment, while others have different koma that can cover different alignments. (e.g. Jotaro has two 5komas, one Power (Red) and one Knowledge (Green).)