[From the notes of Emily Moore. Modified slightly by Sam Rebelsky.]
The following technique was widely used in medieval Europe. Knowing how to multiply two numbers less than 6, you can multiply two numbers between 5 and 10. The process is based on a single-hand representation of numbers between 5 and 10. To represent a number, N, you hold down N-5 fingers.
Here's the strategy, as it was told to me.
Open both palms towards you. To calculate 7 times 9, say, put two fingers down on the left hand (7-5 is 2) and put four fingers down on the right (9-5 is four). Count the number of down fingers (4+2=6) and multiply together the number of up fingers (3 times 1 = 3) and put the two answers together (63). When the number that should be the ones digit is larger than 9, you will have to carry to the tens digit.
Does this work for any two numbers between 5 and 10? Stuck? You may want to try other products to get a better understanding. You may also want to assign variables to quantities in the problem.