Let's simplify the given expression step by step:

$\frac{8 + 3 \left[ (16 + 2^3) \div 6 + 8 \right]}{2}$

Step 1: Simplify the exponent

$2^3 = 8$ So, the expression inside the brackets becomes: $(16 + 8) \div 6 + 8$

Step 2: Simplify addition inside the parentheses

$16 + 8 = 24$ Now the expression is: $24 \div 6 + 8$

Step 3: Perform division

$24 \div 6 = 4$ Now the expression is: $4 + 8$

Step 4: Simplify addition inside the brackets

$4 + 8 = 12$ Now the entire expression simplifies to: $\frac{8 + 3(12)}{2}$

Step 5: Multiply

$3 \times 12 = 36$ So the expression becomes: $\frac{8 + 36}{2}$

Step 6: Simplify addition

$8 + 36 = 44$ Now the expression is: $\frac{44}{2}$

Step 7: Perform division

$44 \div 2 = 22$

Final Answer:

$\boxed{22}$

Would you like me to explain any step in more detail? Here are 5 related questions to expand your understanding:

1. How would the solution change if the exponent were $2^4$ instead of $2^3$?
2. What happens if the division operator is replaced with multiplication in this expression?
3. Can you simplify a similar expression with more nested brackets?
4. How does the order of operations (PEMDAS) affect this calculation?
5. What if the denominator was a different number, like 4 instead of 2?

Tip: Always remember to follow the order of operations (PEMDAS/BODMAS) when simplifying expressions.