Answer: D. $49$

Explanation:1. **Understand the problem:** We are given a function $f(x)=4\sqrt{x}$ and a specific value for $f(x)$, which is $28$. We need to find the value of $x$ that produces this function value.

2. **Set up the equation:** We are given $f(x)=28$. Substitute the definition of $f(x)$: $4\sqrt{x} = 28$

3. **Solve for $\sqrt{x}$:** Divide both sides of the equation by $4$: $\sqrt{x} = \dfrac{28}{4}$ $\sqrt{x} = 7$

4. **Solve for $x$:** To eliminate the square root, square both sides of the equation: $(\sqrt{x})^2 = 7^2$ $x = 49$

5. **Check the solution:** If $x=49$, then $f(49) = 4\sqrt{49} = 4 \times 7 = 28$. This matches the given condition.

6. **Conclusion:** The value of $x$ for which $f(x)=28$ is $49$.