Let's simplify the expression step by step:

We are given the expression:

$4\sqrt{27} \times 2\sqrt{32} \div \sqrt{48}$

Step 1: Simplify each square root term.

1. $\sqrt{27} = \sqrt{9 \times 3} = 3\sqrt{3}$
2. $\sqrt{32} = \sqrt{16 \times 2} = 4\sqrt{2}$
3. $\sqrt{48} = \sqrt{16 \times 3} = 4\sqrt{3}$

Step 2: Substitute the simplified square root terms back into the expression.

$4(3\sqrt{3}) \times 2(4\sqrt{2}) \div 4\sqrt{3}$

This simplifies to:

$12\sqrt{3} \times 8\sqrt{2} \div 4\sqrt{3}$

Step 3: Simplify the division by $4\sqrt{3}$.

First, divide $12\sqrt{3}$ by $4\sqrt{3}$:

$\frac{12\sqrt{3}}{4\sqrt{3}} = 3$

Now the expression becomes:

$3 \times 8\sqrt{2} = 24\sqrt{2}$

Final Answer:

$24\sqrt{2}$

Would you like a more detailed explanation or have any questions?

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Here are 5 related questions for further practice:

1. Simplify: $3\sqrt{50} \times 2\sqrt{18} \div \sqrt{8}$
2. Simplify: $5\sqrt{20} + 3\sqrt{45}$
3. Solve: $\frac{\sqrt{72}}{\sqrt{18}}$
4. Simplify: $7\sqrt{27} \times 2\sqrt{12}$
5. Simplify: $\sqrt{128} \div \sqrt{2}$

Tip: When simplifying square roots, always factor the number under the root into its prime factors to identify perfect squares.