The problem involves translating the graph of $f(x) = -|x|$ to obtain the graph of $g(x)$.

Step-by-Step Solution:

1. Identify the original function $f(x)$:

   • $f(x) = -|x|$ is a "V"-shaped graph opening downward with its vertex at $(0, 0)$.

2. Observe the translation:

   • Looking at the graph of $g(x)$, the vertex has moved:
     • 4 units to the right (from $x = 0$ to $x = 4$).
     • 6 units up (from $y = 0$ to $y = 6$).

3. Apply the translations to the function:

   • A horizontal translation to the right by $h$ units is represented as $|x - h|$.
   • A vertical translation upward by $k$ units is represented as adding $k$ to the function.

   Combining these: $g(x) = -|(x - 4)| + 6$

Final Answer:

The expression for $g(x)$ is: $g(x) = -|x - 4| + 6$

Would you like me to explain translations further or verify specific steps? Here are 5 related questions to explore further:

1. How do vertical and horizontal translations affect a graph?
2. What would happen if the graph were shifted left instead of right?
3. How do you reflect and translate functions at the same time?
4. How can you identify translations directly from an equation?
5. What is the effect of changing the slope of the absolute value function?

Tip: When translating a graph, changes to the $x$-coordinate occur inside the absolute value, while changes to the $y$-coordinate occur outside.