We will simplify the given expression step by step:

\[
\frac{4\sqrt{12}}{3\sqrt{4}}
\]

### Step 1: Simplify Square Roots
- $\sqrt{12} = \sqrt{4 \times 3} = \sqrt{4} \times \sqrt{3} = 2\sqrt{3}$.
- $\sqrt{4} = 2$.

Now, substituting these values into the expression:

\[
\frac{4(2\sqrt{3})}{3(2)}
\]

### Step 2: Simplify the Expression
\[
\frac{8\sqrt{3}}{6}
\]

Since both numerator and denominator are divisible by 2:

\[
\frac{4\sqrt{3}}{3}
\]

### Final Answer:
\[
\frac{4\sqrt{3}}{3}
\]

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

Here are five related problems to try:  
1. Simplify $ \frac{5\sqrt{18}}{2\sqrt{2}} $.  
2. Evaluate $ \frac{6\sqrt{27}}{3\sqrt{9}} $.  
3. Simplify $ \frac{\sqrt{50}}{\sqrt{2}} $.  
4. Rationalize and simplify $ \frac{8}{\sqrt{5}} $.  
5. Simplify $ \frac{10\sqrt{8}}{4\sqrt{2}} $.  

### Tip:  
When simplifying square roots, look for perfect square factors to break them down easily.

The query submitted by the user: $$ \frac{4\sqrt{12}}{3\sqrt4} $$

Learn how to simplify the expression $$ \frac{4\sqrt{12}}{3\sqrt4} $$ step by step. This problem covers simplifying square roots and fractions, making it perfect for students in Grades 6-8.

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