To write the equation based on the description:

1. Original function: $f(x) = \sqrt{x}$.
2. Shifted 6 units to the left: Replace $x$ with $x+6$, giving $f(x) = \sqrt{x+6}$.
3. Reflected in the x-axis: Multiply the entire function by $-1$, resulting in $f(x) = -\sqrt{x+6}$.
4. Reflected in the y-axis: Replace $x$ with $-x$, yielding $f(x) = -\sqrt{-x+6}$.

The final equation is:

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

Would you like further clarification or examples related to this transformation? Here are 5 questions to explore further:

1. How do reflections over the x-axis and y-axis affect the domain and range of functions?
2. How does shifting a function horizontally differ from a vertical shift in terms of notation?
3. What is the domain of the final function $f(x) = -\sqrt{-x+6}$?
4. How would this function be graphed step by step?
5. Can you identify any other transformations combined in different ways for the square root function?

Tip: When dealing with transformations, always apply them step by step in the order specified to avoid confusion.