I thought it might make an interesting post to explain how it works. Every part of this trick matches exactly what you were taught to do in elementary school. Check out the following example:
The blue lines in the image above correspond to the digits of 123 and the red lines correspond to the digits of 321. The place where any two lines intersect is exactly where you were taught to put the product of the two corresponding digits. Of course, the product of two digits is the number of times their corresponding lines intersect.
If you think about it, it is easy to see that this method works for any numbers, but you wouldn’t want to multiply 987 × 789 this way! It is also not hard to see that the lines method will almost always be slower, although it might be easier for students to remember.