To simplify the expression given, follow these steps:
Expression:
[tex]\[
(6x^2 + 8x - 3) - (3x^2 - 6)
\][/tex]
Step 1: Distribute the negative sign through the second parenthesis:
[tex]\[
6x^2 + 8x - 3 - 3x^2 + 6
\][/tex]
Step 2: Combine like terms:
- Combine the [tex]\(x^2\)[/tex] terms:
[tex]\[
6x^2 - 3x^2 = 3x^2
\][/tex]
- Combine the [tex]\(x\)[/tex] terms (there's only one [tex]\(x\)[/tex] term, so it remains the same):
[tex]\[
8x
\][/tex]
- Combine the constant terms:
[tex]\[
-3 + 6 = 3
\][/tex]
Step 3: Put the simplified expression together:
[tex]\[
3x^2 + 8x + 3
\][/tex]
Therefore, the simplified expression is:
[tex]\[
3x^2 + 8x + 3
\][/tex]
The correct answer is [tex]\( \boxed{D} \)[/tex].
