To understand whether (x+3)(x-3) > x^2 + 4x - 2, let's first expand the left side and simplify the right side:

(x+3)(x-3) = x^2 - 3x + 3x - 9 = x^2 - 9

So, we now have the inequality x^2 - 9 > x^2 + 4x - 2.

Rearranging the terms, we get:

0 > 4x - 11

Adding 11 to both sides, we get:

11 > 4x

Dividing both sides by 4, we get:

11/4 > x

Therefore, the inequality (x+3)(x-3) > x^2 + 4x - 2 is true for all values of x such that x < 11/4.