Let's simplify the expression step by step:

\[
4y - \left[13x - 2(y - 2)\right] - 18y
\]

1. First, simplify the expression inside the brackets:

\[
2(y - 2) = 2y - 4
\]

So the expression becomes:

\[
4y - \left[13x - (2y - 4)\right] - 18y
\]

2. Distribute the negative sign across the terms inside the brackets:

\[
4y - \left(13x - 2y + 4\right) - 18y
\]

3. Now, distribute the negative sign across the terms inside the brackets:

\[
4y - 13x + 2y - 4 - 18y
\]

4. Finally, combine like terms:

\[
(4y + 2y - 18y) - 13x - 4
\]

Simplifying further:

\[
-12y - 13x - 4
\]

So, the simplified expression is:

\[
-12y - 13x - 4
\]

Would you like further details or have any questions? 

Here are 5 related questions:

1. How do you simplify expressions with multiple brackets?
2. What is the distributive property in algebra?
3. How do you combine like terms in algebraic expressions?
4. How do you solve linear equations with two variables?
5. How do you handle expressions with negative signs?

**Tip:** When simplifying expressions, always start by dealing with the innermost brackets and then work your way outward.

Learn how to simplify the expression 4y - [13x - 2(y - 2)] - 18y step-by-step with detailed explanations and examples. This problem covers algebraic simplification techniques, including distributing terms and combining like terms. Suitable for students in Grades 7-9.

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