Basically, you take your two numbers which you want to multiply, and write them side by side as two columns. The number on the right is doubled, and the number on the left is halved until you reach 1. If the number on the left is odd then you simple subtract one and then halve it.

So say we take 18 and 21, you would get a table like this:

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`18 21`

9 42

4 84

2 168

1 336

Once you have this table, you cross off all the rows in which the number on the left is even, so now we're left with:

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` 9 42`

1 336

And then you simply add up the numbers in the right hand column, so we have:

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`42 + 336 = 378`

Which you can easily verify on a calculator.

The great thing about this is that because you're halving the number on the left each time it doesn't take long to reach 1 (if your smallest number is 2047 or less it will take at most 10 steps), so you can very quickly multiply very large numbers and it doesn't require any difficult maths really