To construct the equation based on your description:

1. Start with the original function: $f(x) = \sqrt{x}$.
2. Shift the graph 6 units to the left: Replace $x$ with $x + 6$, so we get $f(x) = \sqrt{x + 6}$.
3. Reflect across the x-axis: Multiply the function by $-1$, resulting in $f(x) = -\sqrt{x + 6}$.
4. Reflect across the y-axis: Replace $x$ with $-x$, resulting in the final function:

$f(x) = -\sqrt{-x + 6}$

This is the equation for the described transformation of $f(x) = \sqrt{x}$.

Would you like more details or have any questions? Here are five related questions to deepen understanding:

1. How does shifting a function left or right affect its domain?
2. What happens to the range of $f(x)$ when it's reflected across the x-axis?
3. How does a reflection across the y-axis impact the behavior of the function?
4. How would a vertical shift influence the shape and position of $f(x)$?
5. What are the differences between absolute value transformations and reflections?

Tip: When transforming functions, always apply horizontal changes (shifts and reflections) before vertical transformations.