To find the value of $x$ for which $g(x) = -2$, we can inspect the graph.

Looking at the graph, we identify where the value of $g(x)$ reaches -2 on the y-axis. The graph shows that when $g(x) = -2$, the corresponding $x$-coordinate is $x = 4$.

Thus, the value of $x$ when $g(x) = -2$ is $x = 4$.

Would you like more details on how to interpret the graph or have any additional questions?

Here are some follow-up questions you might find interesting:

1. How can you find the slope of the line from the graph?
2. What does the function $g(x)$ represent in this graph?
3. How can you write an equation for the line based on the graph?
4. What is the behavior of $g(x)$ as $x$ approaches positive infinity?
5. How would the graph change if the value of $g(x)$ shifted up or down by 3 units?

Tip: When analyzing graphs, always pay attention to key points such as intercepts and points where the function crosses specific y-values for more clarity.