Answer: 4^x+5x-2
Add up the equations and combine any like terms. In this case, the like terms are -8 and +6 which combine to -2. Everything else is unlike terms so you leave them as is.
f(x) + g(x) = (4^x-8) + (5x+6)
f(x) + g(x) = 4^x + 5x + (-8+6)
f(x) + g(x) = 4^x + 5x - 2