Japanese kids learn to multiply with a completely different method than the one you probably used as a kid. The Japanese maths voodoo/magic is more of a visual technique that involves drawing lines and counting the intersections.
The video above illustrates the basic method behind these magic lines. You draw lines on the diagonal to represent the numbers of the first number to multiply, then cross those lines with the other number's lines. Add up the intersections for each area, and you have the correct total.
I don't know how or why this works. But it's a pretty amazing trick and might make you wonder why we don't teach maths the way Japanese teachers do. If you want to learn more, Magical Maths showcases another YouTube video with this amazing method.