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.