Let's solve the given expression step by step:

$\left( \frac{80}{5 \times 2} + 12 \right) + \frac{24}{3}$

Step 1: Solve inside the parentheses.

Inside the parentheses, calculate $5 \times 2 = 10$, so the expression becomes: $\left( \frac{80}{10} + 12 \right) + \frac{24}{3}$

Step 2: Divide $80$ by $10$:

$\frac{80}{10} = 8$ Now the expression is: $(8 + 12) + \frac{24}{3}$

Step 3: Add $8 + 12$:

$8 + 12 = 20$ Now the expression becomes: $20 + \frac{24}{3}$

Step 4: Divide $24$ by $3$:

$\frac{24}{3} = 8$

Step 5: Add $20 + 8$:

$20 + 8 = 28$

Thus, the final result is: $\boxed{28}$

Would you like any more details or have further questions? Here are 5 questions to consider:

1. How does the order of operations (PEMDAS) influence solving this type of problem?
2. What would the result be if we changed the division operation to multiplication in the expression?
3. How do parentheses affect the calculation in multi-step expressions like this?
4. What happens if the numbers in the expression are fractions instead of whole numbers?
5. Can you explain how to approach similar expressions with variables?

Tip: Always solve expressions inside parentheses first when following the order of operations.