1. **State the problem:** Simplify the expression $3x(x+4)(x-4)$. 2. **Recall the formula:** The expression involves a product of terms including a difference of squares: $(x+4)(x-4) = x^2 - 16$. 3. **Apply the difference of squares:** Replace $(x+4)(x-4)$ with $x^2 - 16$. So the expression becomes $3x(x^2 - 16)$. 4. **Distribute $3x$:** Multiply $3x$ by each term inside the parentheses: $$3x \cdot x^2 = 3x^3$$ $$3x \cdot (-16) = -48x$$ 5. **Write the simplified expression:** $$3x^3 - 48x$$ 6. **Final answer:** The simplified form of $3x(x+4)(x-4)$ is $$\boxed{3x^3 - 48x}$$