Let's get one things straight. Six Pack to Core is like Windshield to Car Windows. Sure it's right up there in front and it's the first thing to catch the eye. And it can stop the wind and other elements if they are coming directly from the front. But what if they are coming from other directions?
The Core Muscles
Same is with the core muscles. There are many. During any given time, that a kick or a punch is thrown, they are activated in combinations, sometimes at the same time, sometimes in sequence. Depending on the technique.
Training the Core
The most common way to train the core is to do crunches and/or sit ups. It has been this way for years. In the last 15 years or so planks became more popular.
However, do those exercise resemble anything close to the core usage during kicks? Forget biomechanically or Kinesiologically. Think visually. No they do not. And while a six pack may look nice, it does not mean the kick or punch or throw will be improved.
Please take a look at this video and see how the core should be trained for kicking.