Let's simplify the expression step by step:

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

Step 1: Simplify the square roots

1. $\sqrt{12}$ can be simplified: $\sqrt{12} = \sqrt{4 \times 3} = \sqrt{4} \times \sqrt{3} = 2\sqrt{3}$

2. $\sqrt{4} = 2$

Step 2: Substitute the simplified square roots into the expression

$\frac{4\sqrt{12}}{3\sqrt{4}} = \frac{4 \times 2\sqrt{3}}{3 \times 2}$

Step 3: Simplify further

$= \frac{8\sqrt{3}}{6}$

Step 4: Reduce the fraction

Both the numerator and the denominator have a common factor of 2: $\frac{8\sqrt{3}}{6} = \frac{4\sqrt{3}}{3}$

So, the simplified expression is: $\frac{4\sqrt{3}}{3}$

Let me know if you'd like further explanation or have additional questions!

Related Questions:

1. How would you simplify $\frac{\sqrt{50}}{\sqrt{2}}$?
2. What is the general rule for simplifying square roots of products (like $\sqrt{ab}$)?
3. How do you simplify expressions with cube roots instead of square roots?
4. What are some strategies for simplifying complex fractions like the one above?
5. How does rationalizing the denominator work, and when is it used?

Tip: When simplifying square roots, always try to break down the number under the square root into factors that include perfect squares for easier simplification.