I guess for this to work you have to take any column that is greater than 9 and carry the tens digit back up to the higher column. Then, if that column becomes greater than 9 you have to carry that tens up to the next column.

This wasn't automatically clear to me until I ran through 123x456 and figured out that to get the right answer I had to really figure out what was going on with the carried digit.

I'm sure lots of other people figured that out on their own...takes me a minute.