\(\frac{5w-8}{3}=4w+2\ \ \ \ \ |multiply\ both\ sides\ by\ 3\\\\5w-8=3(4w+2)\\\\5w-8=3(4w)+3(2)\\\\5w-8=12w+6\ \ \ \ \ |add\ 8\ to\ both\ sides\\\\5w=12w+14\ \ \ \ \ |subtract\ 12w\ from\ both\ sides\\\\-7w=14\ \ \ \ \ |divide\ both\ sides\ bhy\ (-7)\\\\\boxed{w=-2}\)