The parent function is $y = |x|$. Let's apply each transformation step-by-step:

1. Shift right by 3 units: Replace $x$ with $x - 3$, giving $y = |x - 3|$.
2. Stretch by a factor of 3: Multiply by 3, yielding $y = 3|x - 3|$.
3. Shift down by 2 units: Subtract 2, resulting in $y = 3|x - 3| - 2$.
4. Reflect across the x-axis: Multiply by -1, giving the final equation $y = -3|x - 3| - 2$.

So, the correct answer is the first option: $y = -3|x - 3| - 2$.

Would you like further clarification on any step? Here are 5 related questions to deepen your understanding:

1. What would happen if we shifted left instead of right?
2. How does changing the stretch factor affect the graph?
3. What if we reflected across the y-axis instead?
4. How do vertical and horizontal shifts interact with reflections?
5. How does each transformation affect the vertex of the absolute value function?

Tip: Always apply transformations in the given order to avoid errors.