Answer :

Certainly! Let's find the product of [tex]\(3x\left(x^2 + 4\right)\)[/tex] step-by-step.

### Step 1: Understand the Expression
We are given the expression:
[tex]\[ 3x(x^2 + 4) \][/tex]

### Step 2: Apply the Distribution Property
Using the distributive property of multiplication over addition, we'll multiply [tex]\(3x\)[/tex] by each term inside the parentheses:

[tex]\[ 3x \cdot x^2 + 3x \cdot 4 \][/tex]

### Step 3: Perform Multiplications
Let's do these multiplications one by one:

1. Multiply [tex]\(3x\)[/tex] by [tex]\(x^2\)[/tex]:
[tex]\[ 3x \cdot x^2 = 3x^3 \][/tex]

2. Multiply [tex]\(3x\)[/tex] by [tex]\(4\)[/tex]:
[tex]\[ 3x \cdot 4 = 12x \][/tex]

### Step 4: Combine the Results
Now, we add these two results together:

[tex]\[ 3x^3 + 12x \][/tex]

### Conclusion
The product of [tex]\(3x(x^2 + 4)\)[/tex] is:

[tex]\[ 3x^3 + 12x \][/tex]

So, the correct option is:

[tex]\(\boxed{3x^3 + 12x}\)[/tex]