Let's go over the problems one by one and solve them.

Problem a:

$-32 \div -4 + 3 \times -2$

1. First, solve the division: $-32 \div -4 = 8$
2. Next, solve the multiplication: $3 \times -2 = -6$
3. Finally, add the results: $8 + (-6) = 8 - 6 = 2$ Answer: 2

Problem b:

$-2 \times 5 - 45 \div -9$

1. First, solve the multiplication: $-2 \times 5 = -10$
2. Next, solve the division: $-45 \div -9 = 5$
3. Finally, subtract: $-10 - 5 = -15$ Answer: -15

Problem c:

$8 \times 9 + 4 \times -5$

1. First, solve both multiplications: $8 \times 9 = 72$ $4 \times -5 = -20$
2. Now, add the results: $72 + (-20) = 72 - 20 = 52$ Answer: 52

Problem d:

$-42 \div 7 - 48 \div 8$

1. First, solve both divisions: $-42 \div 7 = -6$ $48 \div 8 = 6$
2. Now, subtract the results: $-6 - 6 = -12$ Answer: -12

Do you want more details on any step or have any questions?

Here are 5 related questions:

1. How do you handle negative numbers in multiplication and division?
2. Can you explain the order of operations (BIDMAS/PEMDAS)?
3. What happens when you add or subtract negative numbers?
4. How does division by negative numbers work?
5. How can you simplify expressions involving both addition and multiplication?

Tip: Always remember to follow the correct order of operations to avoid mistakes when solving mixed operations!