When g (x) is divided by x + 4 the remainder is 0. Given g (x) = x^4+3x^3-6x+8 which conclusion about g (x) is true?

Check your textbook on the Remainder Theorem.

any divisor that yields a remainder of 0 from the dividend, IS a factor of the dividend.

namely, if x⁴+3x³-6x+8 : x+4, gives a remainder of 0, then x+4 IS a factor of x⁴+3x³-6x+8.