Let the numbers be a and b. So a-b=15 where a is the larger number.
8 added to twice the greater number is 2a+8; 4 less than 3 times the lesser number is 3b-4.
These two quantities are equal so 2a+8=3b-4; rearranging this we get 3b-2a=12.
So now we have a system of two equations involving two variables a and b.
We can write b=a-15 and then substitute for b in the other equation:
3(a-15)-2a=12; 3a-45-2a=12, a=12+45=57, so b=57-15=42.
Let's see if this is right.
2a+8=122; 3b-4=122, so the numbers are 57 and 42.