1. To simplify the expression (x^2 + 8x + 12)(x^2 + 12x + 32) + 16, we can expand the two binomials and then combine like terms:

(x^2 + 8x + 12)(x^2 + 12x + 32) + 16
= x^2(x^2 + 12x + 32) + 8x(x^2 + 12x + 32) + 12(x^2 + 12x + 32) + 16
= x^4 + 12x^3 + 32x^2 + 8x^3 + 96x^2 + 256x + 12x^2 + 144x + 384 + 16
= x^4 + 20x^3 + 140x^2 + 400x + 400

Therefore, the simplified expression is x^4 + 20x^3 + 140x^2 + 400x + 400.

2. To simplify the expression (x^2 + 6x + 8)(x^2 + 8x + 15) - 24, we can expand the two binomials and then combine like terms:

(x^2 + 6x + 8)(x^2 + 8x + 15) - 24
= x^2(x^2 + 8x + 15) + 6x(x^2 + 8x + 15) + 8(x^2 + 8x + 15) - 24
= x^4 + 8x^3 + 15x^2 + 6x^3 + 48x^2 + 90x + 8x^2 + 64x + 120 - 24
= x^4 + 14x^3 + 71x^2 + 154x + 96

Therefore, the simplified expression is x^4 + 14x^3 + 71x^2 + 154x + 96.

3. To simplify the expression (x^2 + 4x + 3)(x^2 + 6x + 8) - 24, we can expand the two binomials and then combine like terms:

(x^2 + 4x + 3)(x^2 + 6x + 8) - 24
= x^2(x^2 + 6x + 8) + 4x(x^2 + 6x + 8) + 3(x^2 + 6x + 8) - 24
= x^4 + 6x^3 + 8x^2 + 4x^3 + 24x^2 + 32x + 3x^2 + 18x + 24 - 24
= x^4 + 10x^3 + 35x^2 + 50x

Therefore, the simplified expression is x^4 + 10x^3 + 35x^2 + 50x.