Let's simplify the expression step by step:

$(7x^2 - 6x + 2) - (4x - 8) + (-6x^2 + 3x)$

1. First, distribute the negative signs: $7x^2 - 6x + 2 - 4x + 8 - 6x^2 + 3x$

2. Now, combine like terms:

• $7x^2$ and $-6x^2$:
  $7x^2 - 6x^2 = x^2$

• $-6x$, $-4x$, and $3x$:
  $-6x - 4x + 3x = -7x$

• Constants $2$ and $8$:
  $2 + 8 = 10$

So, the simplified expression is: $x^2 - 7x + 10$

Would you like more details on any step or have further questions?

Here are some related questions for further practice:

1. How do you factor a quadratic expression like $x^2 - 7x + 10$?
2. Can you find the roots of $x^2 - 7x + 10$?
3. How do you complete the square for $x^2 - 7x + 10$?
4. What is the discriminant of $x^2 - 7x + 10$ and what does it tell you?
5. How would the expression change if a term was raised to a higher degree (e.g., $x^3$)?

Tip: Always double-check for like terms when simplifying complex expressions; it helps avoid mistakes!