1. The problem is to factor the expression $12x^2 + 8$. 2. To factor an expression, we look for the greatest common factor (GCF) of the terms. 3. The terms are $12x^2$ and $8$. The GCF of $12$ and $8$ is $4$. 4. Factor out $4$ from each term: $$12x^2 + 8 = 4(\frac{12x^2}{4} + \frac{8}{4})$$ 5. Simplify inside the parentheses: $$4(3x^2 + 2)$$ 6. This matches option B. Therefore, the factored form of $12x^2 + 8$ is $4(3x^2 + 2)$.