When multiplying any single digit number with nine, use the finger trick. Hold both of your hands out in front of you so that the palms are facing away. Then, counting from left to right, identify the finger that corresponds to the number you are multiplying with nine. The fingers left up on the left side of the lowered finger represent the tens digit of the answer while the ones on the right represent the ones digit. For instance, in 9 x 6, you would hold down the sixth finger to get 5 fingers on the left and 6 on the right, indicating 56.
When multiplying a one digit number with a two digit number, break the two digit number into its tens component and its ones component to make the problem easier. For example, think of 7(17) as 7(10 + 7), as though you are distributing the seven. By doing the two simpler multiplication problems in your head, you can then add them together to get the final result. In this example, you would add 70 and 49 to get 119.
When multiplying 8 with any number, you can use the fact that 8 is 2 less than 10 to re-think the problem. Thus, you multiply 10 with the number and then subtract what 2 times the number is to get the answer. For example, with 8 x 12, you would multiply 10 x 12 = 120 and then subtract 2 x 2 = 24 to wind up with 96.
This technique works when you need to multiply a number by 4. To use it, double the number you are multiplying 4 with once. Then, double the result again. For example, when performing 4 x 15, you would double 15 to get 30. Then, you would double 30 to get the correct answer of 60.
There are two different tricks for multiplying numbers by 11. Which you want to use depends on the number in the problem. If you are multiplying 11 with a number between 1 and 10, just double the digit of the latter number. For example, 11 x 3 = 33 and 11 x 6 = 66. However, for numbers between 10 and 18, use a different tactic. For these, use the digits of the number and insert their sum between them. For instance, 11 x 13 would be 1 (1 +3) 3 which changes to 143.