The opposite of any number is negative that number.
The opposite of x is -x.

Twice the opposite of any number is double that number's negative value.
Twice the opposite of x is 2*-x.

Twenty four greater than twice the opposite of a number is that number's doubled negative value plus twenty four.
Twenty four greater than twice the opposite of x is (2*-x)+24

Let's simplify:
-2x+24
...that was easy.

Well, we want a number that is twice its opposite plus 24, so the number X must equal the equation:
x=-2x+24

There, now we solve:
x=-2x+24  plus 2x on both sides
x+2x=-2x+24+2x  the 2x and -2x on the right cancel and on the left add up:
3x=24  divide both sides by 3
x=8.   

There's the answer.

8 is twenty four more than twice its opposite:
8=(-2*8)+24
8=(-16)+24
8=24-16
8=8  Woopee!!!

ok if you have questions or concerns feel free to email me.