Let's break down the expression step by step:

$[(21 + 6) - 32] \div 9 \times 2$

1. First, solve inside the brackets: $21 + 6 = 27$ So the expression becomes: $(27 - 32) \div 9 \times 2$

2. Now, perform the subtraction: $27 - 32 = -5$ So the expression is now: $-5 \div 9 \times 2$

3. Next, perform the division: $-5 \div 9 = -\frac{5}{9} \approx -0.555$ So the expression becomes: $-0.555 \times 2$

4. Finally, perform the multiplication: $-0.555 \times 2 = -1.11$

Rounding to the nearest value, the closest answer is 1.

Final answer: 1

Would you like more details on any step?

Here are some related questions:

1. How do you handle division of negative fractions?
2. What are the rules for the order of operations (PEMDAS)?
3. How do you round numbers to the nearest integer?
4. How do you multiply decimal numbers by whole numbers?
5. Can you explain how negative numbers interact with division and multiplication?

Tip: Always apply the order of operations (PEMDAS: Parentheses, Exponents, Multiplication and Division, Addition and Subtraction) to solve expressions correctly.