It looks like you're asking about the expression:

$3 \sqrt{12x^3 - 4x^3}$

Let's break it down step-by-step:

Step 1: Combine Like Terms

First, let's combine the terms inside the square root. Both terms have $x^3$, so we can factor that out:

$12x^3 - 4x^3 = (12 - 4)x^3 = 8x^3$

So the expression becomes:

$3 \sqrt{8x^3}$

Step 2: Simplify the Square Root

Now we simplify the square root. We can break down the square root of the product:

$\sqrt{8x^3} = \sqrt{8} \cdot \sqrt{x^3}$

We know that:

$\sqrt{8} = \sqrt{4 \cdot 2} = 2\sqrt{2}$ And:

$\sqrt{x^3} = x^{3/2} = x \cdot \sqrt{x}$

So the expression becomes:

$3 \cdot 2\sqrt{2} \cdot x \cdot \sqrt{x} = 6x \sqrt{2x}$

Final Answer:

$6x \sqrt{2x}$

Let me know if you need more details on any of the steps or have additional questions!

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Here are some related questions to explore:

1. How would you simplify other expressions involving square roots and powers?
2. What are the properties of square roots that can be useful in simplifying expressions?
3. How do you handle simplifying cube roots?
4. Can you factor expressions with cubes and square roots together?
5. What happens if you apply the distributive property to an expression like this?

Tip: When dealing with roots and exponents, remember to break down the terms into prime factors or factor out common powers to make simplifications easier!