By performing a task that is counter intuitive with being emotionally charged you give your whole body a chance to calm down. The adrenaline that your brain pumps into your system during periods of high emotions is eased back to normal levels. This lets your shoulders, abdominal muscles, and legs fall into a more comfortable state of being. A relaxed body has a harder time being emotionally engaged in negative interaction.
Many people find that they can start the Panda Coloring Book page with a great deal of anger reflected in their strokes. You can often see the difference from the harder, less intentional strokes of the crayon to the softer and more reserved strokes. This is visually satisfying because you can see that it is working. As you start to see the pattern of strokes from one end of the book to the other, you will notice that it takes less time for the hard strokes to soften.