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The problem presented is:

\[
(8x^2 - 4x - 3) + (-2x^2 - 3x + 9)
\]

We need to simplify this expression by combining like terms.

### Step 1: Combine the \(x^2\) terms.
\[
8x^2 + (-2x^2) = 6x^2
\]

### Step 2: Combine the \(x\) terms.
\[
-4x + (-3x) = -7x
\]

### Step 3: Combine the constant terms.
\[
-3 + 9 = 6
\]

### Final Expression:
\[
6x^2 - 7x + 6
\]

Therefore, the correct option is **A: \(6x^2 - 7x + 6\)**.

Would you like any more details, or have any questions?

Here are 5 related questions to further your understanding:
1. How do you handle subtraction between polynomials?
2. What is the difference between adding polynomials and multiplying polynomials?
3. How do you factor the polynomial \(6x^2 - 7x + 6\)?
4. Can you add polynomials with different numbers of terms?
5. What are the rules for combining like terms?

**Tip:** Always align terms by their degree (e.g., \(x^2\), \(x\), and constants) to simplify addition and subtraction of polynomials easily.

Learn how to simplify the polynomial expression (8x^2 - 4x - 3) + (-2x^2 - 3x + 9) by combining like terms. This step-by-step guide covers key algebraic concepts and principles of polynomial addition. Suitable for students in Grades 8-10.

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