Answer 15 spiders and 9 beetles

Thank you but how do you find this answer ? ;-)

You can solve using Gues & Check method or Algebra. But I am trying to use assumption method since this is assuptiom topic as show in your picture.

We have found !
So if 24 spiders = 192 legs for spiders and 0 for beetles the difference is 192
If you decrease 1 spider you have 23 spiders = 184 legs for spiders and 6 for one beetle
The difference is 178 (184-6)
Increase 1 beetle = decrease 14 legs (192-178)
So
(192-66)/14 = 9
We have 9 beetles and 15 spiders ;-)

Yes. Well done.
This is correct assumption method.