First, we will expand each set of parentheses:

(2x-3)(x+2) = 2x^2 + 4x - 3x - 6 = 2x^2 + x - 6

(x-4)(x+4) = x^2 + 4x - 4x - 16 = x^2 - 16

Now, we will add the expanded forms together:

(2x^2 + x - 6) + (x^2 - 16) = 2x^2 + x - 6 + x^2 - 16

Now, we will combine like terms:

2x^2 + x - 6 + x^2 - 16 = 3x^2 + x - 6 - 16

3x^2 + x - 22

Therefore, the final expanded expression is 3x^2 + x - 22.