The problem asks for an equation based on the graph of $y = \sqrt{x}$, which undergoes two transformations:

1. Reflection across the origin: This implies a reflection over both the x-axis and y-axis, making the new function $y = -\sqrt{-x}$.

2. Shifted left by 6 units: A horizontal shift to the left means we replace $x$ with $x + 6$.

Combining these two transformations, the new equation becomes:

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

Would you like further clarification or details on these transformations?

Here are 5 questions to explore further:

1. What is the effect of reflecting a function across the y-axis vs the x-axis?
2. How would shifting the graph up or down affect the equation?
3. Can you apply this method to different types of functions, such as $y = x^2$?
4. How do vertical stretches or compressions change the appearance of the graph?
5. What happens when you reflect and shift other types of square root functions, such as $y = \sqrt{x + 2}$?

Tip: To understand how a graph changes with reflections and shifts, it's useful to plot the original and transformed functions on a graphing calculator or tool for a visual comparison.