The problem asks us to simplify the expression $(3x^2 - 2x - 7) - (2x^2 + 6x - 3)$.

1. Problem Description

The problem asks us to simplify the expression $(3x^2 - 2x - 7) - (2x^2 + 6x - 3)$.

2. Solution Steps

First, we distribute the negative sign to the second polynomial:

$(3x^2 - 2x - 7) - (2x^2 + 6x - 3) = 3x^2 - 2x - 7 - 2x^2 - 6x + 3$.

Next, we combine like terms:

$3x^2 - 2x^2 - 2x - 6x - 7 + 3$.

$(3-2)x^2 + (-2-6)x + (-7+3)$.

$1x^2 - 8x - 4$.

3. Final Answer

The simplified expression is $x^2 - 8x - 4$.