The given limit evaluates to:

$\lim_{{x \to 0}} \frac{x}{{\sqrt{4 + x} - 2}} = 4$

Thus, the correct answer is B. 4.

Would you like further details on how the solution was derived?

Here are 5 related questions you can try:

1. What happens if the limit approaches infinity instead of zero?
2. How would you simplify the expression by multiplying by the conjugate?
3. Can you apply L'Hopital's Rule to this limit problem?
4. How would the limit change if the function inside the square root was different?
5. What if $x \to -4$, would the limit still exist?

Tip: When working with square roots in limits, multiplying by the conjugate often simplifies the process!