To solve the expression \( 6 + (-6) \times 3 - (-(4 + 2)) \), follow the order of operations (PEMDAS: Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right)):

1. **Parentheses**: First, solve inside the parentheses:
   \[
   4 + 2 = 6
   \]
   Then the expression becomes:
   \[
   6 + (-6) \times 3 - (-(6))
   \]

2. **Negation inside parentheses**:
   \[
   -(6) = -6
   \]
   Therefore, the expression simplifies to:
   \[
   6 + (-6) \times 3 - (-6)
   \]

3. **Multiplication**: Multiply \(-6\) by \(3\):
   \[
   (-6) \times 3 = -18
   \]
   So the expression becomes:
   \[
   6 + (-18) - (-6)
   \]

4. **Negation**: The expression \(-(-6)\) becomes \(6\):
   \[
   6 + (-18) + 6
   \]

5. **Addition and Subtraction**: Perform the operations from left to right:
   \[
   6 - 18 + 6 = -12 + 6 = -6
   \]

The final answer is \(-6\).

Would you like further explanation or have any questions?

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Here are 5 related questions to further your understanding:

1. What is the result of \( 8 - 4 \times 2 + 3 \)?
2. How would the expression change if there were different signs, such as \( -6 + (-6) \times 3 - (-4 + 2) \)?
3. What is the importance of the order of operations in solving algebraic expressions?
4. Can you evaluate the expression \( 7 - 3(2 + 5) + 9 \)?
5. How would you simplify \( 10 + (-5 \times 4) - 2^2 \)?

**Tip:** Always perform operations inside parentheses first and be careful with the signs when expanding them.

Learn how to solve the expression 6 + (-6) × 3 - (-(4 + 2)) step-by-step with detailed explanations. This problem involves integer operations and understanding the order of operations (PEMDAS). Suitable for students in Grades 6-8.

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