Answer
The area is also $\frac{16}{3}$ square units since $y=\sqrt{-x}$ is just the reflection about the $y$-axis of $y=\sqrt{x}$.
Work Step by Step
Step 1. (Optional, for visual reference only.). Graph $y=\sqrt x$, $y=\sqrt {-x}$, $x=-4$, and $x=4$ as shown in the image below.
Step 2. Notice that $y=\sqrt{-x}$ is the reflection of $y=\sqrt{x}$ about the $y$-axis, while $x=-4$ is the reflection of $x=4$ about the $y$-axis..
Step 3. Thus, the area under $y=\sqrt {-x}$ bounded from below by the $x$-axis and on the left by $x=-4$ equals to the known area which is a symmetric image across the $y$-axis.
Step 4. Thus, the answer is $\frac{16}{3}$ square units.
