To find the product of the binomials [tex]\( (3x + 6)(4x + 2) \)[/tex], we'll follow the standard procedure for multiplying binomials.
1. Identify the terms of the binomials:
[tex]\[
(3x + 6) \quad \text{and} \quad (4x + 2)
\][/tex]
2. Multiply each term in the first binomial by each term in the second binomial:
[tex]\[
(3x + 6)(4x + 2) = (3x \cdot 4x) + (3x \cdot 2) + (6 \cdot 4x) + (6 \cdot 2)
\][/tex]
3. Compute each product separately:
[tex]\[
3x \cdot 4x = 12x^2
\][/tex]
[tex]\[
3x \cdot 2 = 6x
\][/tex]
[tex]\[
6 \cdot 4x = 24x
\][/tex]
[tex]\[
6 \cdot 2 = 12
\][/tex]
4. Combine the resulting terms:
[tex]\[
12x^2 + 6x + 24x + 12
\][/tex]
5. Simplify by combining like terms (the terms with [tex]\( x \)[/tex] in them):
[tex]\[
12x^2 + (6x + 24x) + 12 = 12x^2 + 30x + 12
\][/tex]
So, the product of the binomials [tex]\( (3x + 6)(4x + 2) \)[/tex] is [tex]\( 12x^2 + 30x + 12 \)[/tex].
Thus, the correct answer is:
[tex]\[
\boxed{12x^2 + 30x + 12}
\][/tex]
Therefore, the answer is option B.
