2x^3 - 16x^2 - 6x + 48
= (2x^3 - 16x^2) - (6x - 48)
= (2x^2)(x - 8) - (6)(x - 8)
= (2x^2 - 6)(x - 8)
= 2(x^2 - 3)(x - 8) ----- (1)
= 2(x + sqrt(3))(x - sqrt(3))(x - 8) ------ (2)
Actually (1) should be enough, but if your teacher wants you to really tear everything out , then you will need to go for (2).
Anyway, if you are not sure, you can always check by expanding out the terms.
If you have (2x^2 - 6) and (x + 8), upon expanding out, you will get:
(2x^2 - 6)(x + 8)
= (2x^2)(x) - 6x + 8(2x^2) - (6)(8)
= 2x^3 - 6x + 16x^2 - 48
= 2x^3 + 16x^2 - 6x - 48
Note that this is wrong, since we have + 16x^2 and not - 16x^2