Simplify as
(2x) / (x + 2) = (8x -6) / (x + 4) cross-multiply
2x ( x + 4) = (8x - 6) ( x + 2)
2x^2 + 8x = 8x^2 + 10x - 12 rearrange as
6x^2 + 2x - 12 = 0 divide through by 2
3x^2 + x - 6 = 0
-1 ±√ [ 1^2 - 4 * -6 * 3 ] -1 ±√73
x = _____________________ = __________
2 * 3 6