1. The problem asks for the remainder when the polynomial $p(x) = x^3 - 4x^2 + 6x - 24$ is divided by $x - 2$. 2. According to the Remainder Theorem, the remainder of dividing a polynomial $p(x)$ by $x - a$ is $p(a)$. 3. Here, $a = 2$, so we need to evaluate $p(2)$: $$p(2) = (2)^3 - 4(2)^2 + 6(2) - 24$$ 4. Calculate step-by-step: $$2^3 = 8$$ $$4(2)^2 = 4 \times 4 = 16$$ $$6(2) = 12$$ 5. Substitute these values: $$p(2) = 8 - 16 + 12 - 24$$ 6. Simplify: $$8 - 16 = -8$$ $$-8 + 12 = 4$$ $$4 - 24 = -20$$ 7. Therefore, the remainder is $-20$. Final answer: **b. -20**