Multiply the binomials.

To multiply the binomials \((2x + 1)(3x + 2)\), we can apply the distributive property (also known as the FOIL method for binomials):

1. First, multiply the first terms:
\(2x \cdot 3x = 6x^2\)

2. Next, multiply the outer terms:
\(2x \cdot 2 = 4x\)

3. Then, multiply the inner terms:
\(1 \cdot 3x = 3x\)

4. Finally, multiply the last terms:
\(1 \cdot 2 = 2\)

Now, combine all these results:
\[
6x^2 + 4x + 3x + 2
\]

Combine the like terms (4x and 3x):
\[
6x^2 + 7x + 2
\]

Therefore, the product of the binomials \((2x + 1)(3x + 2)\) is:
\[
\boxed{6x^2 + 7x + 2}
\]