https://file.aiquickdraw.com/mathbot/file/1728960996883xepxehyc.jpg

The expression to evaluate is:

\[
2x - (3x + 2xy - 3y^2)
\]

where \( x = 6 \) and \( y = 2 \).

### Step-by-Step Solution
1. **Substitute** \( x = 6 \) and \( y = 2 \) into the expression:
   \[
   2(6) - (3(6) + 2(6)(2) - 3(2)^2)
   \]

2. **Calculate** each term inside the parentheses:
   - \( 3(6) = 18 \)
   - \( 2(6)(2) = 24 \)
   - \( 3(2)^2 = 3(4) = 12 \)

   So, the expression within the parentheses becomes:
   \[
   18 + 24 - 12
   \]

3. **Simplify** inside the parentheses:
   \[
   18 + 24 - 12 = 30
   \]

4. **Substitute** back to the main expression:
   \[
   2(6) - 30
   \]

5. **Evaluate the remaining terms**:
   - \( 2(6) = 12 \)

   So, the expression is:
   \[
   12 - 30 = -18
   \]

### Final Answer
The evaluated expression is:
\[
\boxed{-18}
\]

Would you like more details on any step? 

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Here are some related questions for practice:
1. What would the result be if \( x = 4 \) and \( y = 3 \) for the same expression?
2. How would the result change if the expression were \( 2x + (3x + 2xy - 3y^2) \)?
3. What are the general steps to evaluate expressions with multiple variables?
4. How does distributing the negative sign affect the terms inside the parentheses?
5. How would you factor the expression \( 3x + 2xy - 3y^2 \)?

**Tip:** Always simplify expressions inside parentheses before applying any operations outside.

Evaluate the expression 2x - (3x + 2xy - 3y^2) when x = 6 and y = 2.

Learn how to evaluate the algebraic expression 2x - (3x + 2xy - 3y^2) when x = 6 and y = 2, using substitution and simplification techniques. This solution walks through key steps in solving algebraic expressions, suitable for Grades 8-10.

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