Let's solve the expression step by step:

Given expression:

\[
\frac{144}{8 - \left[32 - 6 \cdot 6\right) - 9\right] - 9}
\]

### Step 1: Solve inside the brackets and parentheses

First, solve the multiplication within the square brackets:

\[
6 \cdot 6 = 36
\]

Now substitute this into the expression:

\[
\frac{144}{8 - \left[32 - 36) - 9\right] - 9}
\]

### Step 2: Simplify inside the square brackets

Now, subtract within the square brackets:

\[
32 - 36 = -4
\]

Substitute back:

\[
\frac{144}{8 - (-4 - 9) - 9}
\]

### Step 3: Simplify the expression inside the parentheses

Subtract inside the parentheses:

\[
-4 - 9 = -13
\]

Substitute back:

\[
\frac{144}{8 - (-13) - 9}
\]

### Step 4: Simplify further

Subtract and add inside the denominator:

\[
8 - (-13) = 8 + 13 = 21
\]

\[
21 - 9 = 12
\]

Now the expression simplifies to:

\[
\frac{144}{12} = 12
\]

### Final Answer:
The value of the expression is \( \boxed{12} \).

Would you like more details or have any questions? Here are some related questions you might find interesting:

1. How do parentheses and brackets affect the order of operations?
2. What is the distributive property, and how is it applied in algebraic expressions?
3. How can complex fractions be simplified?
4. What are some common pitfalls in solving algebraic expressions?
5. How do you handle negative signs in arithmetic operations?

**Tip:** Always follow the order of operations: Parentheses, Exponents, Multiplication and Division (from left to right), and Addition and Subtraction (from left to right), often remembered by the acronym PEMDAS.

Learn how to solve the arithmetic expression 144 divided by (8 minus [32 minus 6 times 6] minus 9) minus 9 step-by-step. This problem involves arithmetic operations, parentheses, brackets, and negative numbers, suitable for students in Grades 6-8.

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