1. The problem states that the function $g(x) = 8(4^x)$ is reflected across the x-axis to create $f(x)$. We need to find the equation of $f(x)$. 2. Reflection across the x-axis means that every $y$-value of the original function is multiplied by $-1$. This changes the sign of the output values. 3. The formula for reflecting a function $g(x)$ across the x-axis is: $$f(x) = -g(x)$$ 4. Applying this to $g(x) = 8(4^x)$, we get: $$f(x) = -8(4^x)$$ 5. This means the function $f(x)$ is the negative of $g(x)$, flipping it below the x-axis. 6. Therefore, the equation of the reflected function is: $$\boxed{f(x) = -8(4^x)}$$