Clement from Shat Tin College in Hong Kong has sent us a detailed explanation of how to use Napier's Bones to calculate the products in the question:
In order to work out a multiplication such as 8931*6, you need
to first work out 8*6.
Taking the first digit of the 4 digit number and multiplying it by 6 which gives you 48.
You then do the next digit, 9*6 which gives you 54.
You add the first digit of 54: 5 to the last digit of 48: 8. This gives you 13.
You then add the tens digit of 13: 1 to the very first digit: 4 which than gives you a total of 534.
You carry on with 3*6: 18, add the tens digit: 1 to the last digit of the total: 534 giving you 535 and put the unit: 8 at the end. 5358.
The last step is 1*6, adding the answer: 6 to the total: 5358 gives you 53586.
The answer for 461*4 was 1844 and the answer for 24*6 was 144.
The last one was very complicated, 3541*768:
Firstly, you multiply the four digit number, 3541 by the first digit of the 3 digit number, 7. But remember to use Napier's bones to do this multiplication step by step in the way I explained in the first paragraph. You get 24787.
Then multiply 3541 by the next digit of the 3 digit number, 6. This gives you 21246.
The next step is to multiply 3541 by the last digit of the 3 digit number, 8. That makes 28328.
You add this to the previous answer: 21246 starting from the second digit, for example: 21246 + 28328 but keep the 2 at the front of 21246. This makes 240788.
The last step is to add this number to 24787, the first answer, starting from the second digit for example: 24787 + 240788 but keeping the 2 at the front of 24787.
This makes 2719488.
Excellent Clement, you have written a clear explanation which must have been hard without any pictures.