According to the Distributive Property, which expression is expression is equivalent to 4x^3 + 8x^2 + 12x?

To determine which expression is equivalent to \(4x^3 + 8x^2 + 12x\) using the Distributive Property, we need to factor out a common factor from the expression.

The given expression can be factored as follows:
\[
4x^3 + 8x^2 + 12x = 4x(x^2 + 2x + 3)
\]

Now, we can analyze the provided options:

1. \((2x^2 + 4)(2x - 3)\)
2. \(4x(x^2 + 2x + 3)\)
3. \(4x(4x + 5x)\)
4. \((2x^2 + 4)(2x^2 + 3)\)

The correct equivalent expression is **\(4x(x^2 + 2x + 3)\)**, which is option 2.

Now let's quickly evaluate the others for completeness:

1. \((2x^2 + 4)(2x - 3)\) does not simplify to the original expression.
2. \(4x(x^2 + 2x + 3)\) matches our factored expression and is correct.
3. \(4x(4x + 5x) = 4x(9x) = 36x^2\), which does not match.
4. \((2x^2 + 4)(2x^2 + 3)\) does not simplify to the original expression.

Thus, the final answer is:

**\(4x(x^2 + 2x + 3)\)** (Option 2).