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The question asks for the rationalized form of the following expression:

\[
\frac{4\sqrt{5}}{4 - \sqrt{12}}
\]

### Steps to solve:
1. **Simplify the denominator**:  
   Notice that \(\sqrt{12} = \sqrt{4 \times 3} = 2\sqrt{3}\), so the denominator becomes:
   \[
   4 - \sqrt{12} = 4 - 2\sqrt{3}
   \]

2. **Multiply by the conjugate**:  
   To rationalize the denominator, multiply both the numerator and the denominator by the conjugate of the denominator \(4 + 2\sqrt{3}\):
   \[
   \frac{4\sqrt{5}}{4 - 2\sqrt{3}} \times \frac{4 + 2\sqrt{3}}{4 + 2\sqrt{3}} = \frac{4\sqrt{5}(4 + 2\sqrt{3})}{(4 - 2\sqrt{3})(4 + 2\sqrt{3})}
   \]

3. **Simplify the denominator**:
   The denominator becomes a difference of squares:
   \[
   (4 - 2\sqrt{3})(4 + 2\sqrt{3}) = 4^2 - (2\sqrt{3})^2 = 16 - 12 = 4
   \]

4. **Simplify the numerator**:
   Expand \(4\sqrt{5}(4 + 2\sqrt{3})\):
   \[
   4\sqrt{5}(4 + 2\sqrt{3}) = 16\sqrt{5} + 8\sqrt{15}
   \]

5. **Final expression**:
   Now the expression becomes:
   \[
   \frac{16\sqrt{5} + 8\sqrt{15}}{4} = 4\sqrt{5} + 2\sqrt{15}
   \]

Thus, the rationalized form is:
\[
4\sqrt{5} + 2\sqrt{15}
\]

### Answer:
The correct choice is **B**.

---

Would you like more details on any step? Here are some related questions:

1. How do you find the conjugate of a binomial involving square roots?
2. What is the difference between simplifying and rationalizing an expression?
3. How do you expand products involving square roots?
4. Why is it important to rationalize the denominator in some problems?
5. How does the difference of squares formula apply in rationalizing denominators?

**Tip**: When multiplying by the conjugate, always remember that the denominator simplifies using the difference of squares formula.

Bentuk rasional dari \frac{4\sqrt{5}}{4 - \sqrt{12}} adalah ...

Learn how to rationalize the denominator of \frac{4\sqrt{5}}{4 - \sqrt{12}} step-by-step by simplifying square roots and multiplying by the conjugate. This problem is perfect for high school students in grades 10-12, covering core algebraic concepts.

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