Help!! I have an idea of how this works but I’m not 100% sure

The solution is:
x = 12
Explanation:Given the equation:
[tex]\frac{3}{x+3}=\frac{4}{x+8}[/tex]Multiply both sides of the equation by (x + 3)(x + 8)
3(x + 8) = 4(x + 3)
Remove parentheses
3x + 24 = 4x + 12
Subtract 3x from both sides
24 = 4x - 3x + 12
24 = x + 12
Subtract 12 from both sides
x = 24 - 12
= 12