Let's solve each expression step-by-step for $a = 6$ and $b = -4$:

a. $-a + b$

$-a + b = -(6) + (-4) = -6 - 4 = -10$

b. $a - b$

$a - b = 6 - (-4) = 6 + 4 = 10$

c. $2(b - a)$

$2(b - a) = 2((-4) - 6) = 2(-10) = -20$

d. $-ab^2$

$-ab^2 = -(6)(-4)^2 = -(6)(16) = -96$

e. $a^2 + b^2$

$a^2 + b^2 = (6)^2 + (-4)^2 = 36 + 16 = 52$

f. $24 \div (ab)$

$24 \div (ab) = 24 \div (6 \times -4) = 24 \div (-24) = -1$

Summary of the results:

• a. $-a + b = -10$
• b. $a - b = 10$
• c. $2(b - a) = -20$
• d. $-ab^2 = -96$
• e. $a^2 + b^2 = 52$
• f. $24 \div (ab) = -1$

Let me know if you'd like further details or have any questions.

Here are 5 related questions for further practice:

1. What is the value of $a^3 + b^3$ for the same values of $a$ and $b$?
2. Calculate $(a - b)^2$ for $a = 6$ and $b = -4$.
3. What is the value of $a \times (b + a)$?
4. How does $a + b^2$ change if $b = 0$?
5. What is the product of $(a + b) \times (a - b)$?

Tip: Always check if you need to distribute negatives carefully when simplifying expressions involving subtraction or negatives.