To find the equation of the function $h(x)$ based on the transformation steps applied to $f(x) = x^2$, follow these two steps:

1. Shift the graph of $f(x)$ to the right by 6 units:
   Shifting a graph horizontally to the right by $c$ units is done by replacing $x$ with $x - c$. In this case, $c = 6$. So, the equation becomes: $f(x) = (x - 6)^2$

2. Reflect the graph over the y-axis:
   Reflecting a graph over the y-axis is done by replacing $x$ with $-x$. Applying this transformation to $(x - 6)^2$, the equation becomes: $h(x) = (-x - 6)^2$

Thus, the equation of the transformed function is: $h(x) = (-x - 6)^2$

Would you like further clarification on how transformations work or any other details?

Related Questions:

1. What is the effect of shifting a graph left or right on the function's equation?
2. How would you reflect a graph over the x-axis instead of the y-axis?
3. How does a vertical shift affect the function $f(x)$?
4. What transformations preserve the shape of the graph of a function?
5. Can multiple transformations be combined into one equation?

Tip:

Always perform horizontal transformations (shifts and reflections) before vertical ones to avoid confusion.