To transform the graph of $y = |x|$ to match the graph of $y = |x + 3| - 4$, we apply two translations:

1. Horizontal Shift: The expression $|x + 3|$ shifts the graph 3 units to the left.
2. Vertical Shift: The $-4$ outside the absolute value shifts the graph 4 units down.

So, to achieve this transformation, move the original graph of $y = |x|$ 3 units left and 4 units down.

Would you like further details on graph transformations?

Here are some related questions to deepen your understanding:

1. How would the graph change if we used $y = |x - 3| - 4$ instead?
2. What effect does a positive constant outside the absolute value function have on the graph?
3. How do vertical stretches and compressions affect the graph of $y = |x|$?
4. What happens if we replace $x$ with $-x$ inside the absolute value function?
5. How would we graph $y = |x + 3| + 4$?

Tip: When transforming graphs, focus on horizontal and vertical shifts first before considering stretches and reflections.