#### Answer

$$-x^2 + 4x + 8$$

#### Work Step by Step

We are subtracting a polynomial in this problem, so subtracting a polynomial is the same as adding its opposite. We can now rewrite the problem according to this property:
$$(4x^2 - 3x + 2) + (-5x^2 + 7x + 6)$$
Simplify the expression by getting rid of the parentheses:
$$4x^2 - 3x + 2 - 5x^2 + 7x + 6$$
Group like terms:
$$(4x^2 - 5x^2) + (-3x + 7x) + (2 + 6)$$
Combine like terms:
$$-x^2 + 4x + 8$$