Let's solve the expression step by step:

Given: $22 - (8 - 2) + [6 \cdot (20 \div 5) - 11]$

Step 1: Simplify inside the parentheses

First, solve the parentheses:

$8 - 2 = 6$ $20 \div 5 = 4$

Now the expression becomes: $22 - 6 + [6 \cdot 4 - 11]$

Step 2: Perform the multiplication inside the brackets

$6 \cdot 4 = 24$

So the expression becomes: $22 - 6 + [24 - 11]$

Step 3: Simplify inside the brackets

$24 - 11 = 13$

Now the expression is: $22 - 6 + 13$

Step 4: Perform the remaining addition and subtraction

$22 - 6 = 16$ $16 + 13 = 29$

So, the simplified result is: $\boxed{29}$

The correct answer is 29.

Would you like more details on any step or further explanation?

Here are five related questions you might find interesting:

1. How do you handle more complex expressions with multiple nested brackets?
2. What is the order of operations (PEMDAS) and why is it important in solving such problems?
3. How can you simplify expressions with variables instead of numbers?
4. How do negative numbers affect the order of operations?
5. What is the distributive property, and how does it apply to solving equations?

Tip: Always start by simplifying the innermost parentheses or brackets when following the order of operations!