How to factor 6x^3 + 12x^2 + 4x + 8?

I keep getting (6x^2 + 4)(x + 2).

well, you can factor out the 2 and have

2(3x^2+2)(x+2)

3x^2+2 does not factor, since its discriminant is negative. After all, x^2 is always positive, so 3x^2+2 is always positive.