To solve the composite function $f(g(6))$ using the graphs provided:

1. Find $g(6)$:

   • Look at the graph of $g(x)$ (the red line) and locate where $x = 6$.
   • From the graph, it appears that $g(6) = -4$, as the red graph intersects the point $(6, -4)$.

2. Find $f(g(6)) = f(-4)$:

   • Now, using $g(6) = -4$, we need to find $f(-4)$.
   • Look at the graph of $f(x)$ (the blue line) and locate where $x = -4$.
   • From the graph, it seems that $f(-4) = 6$, as the blue graph intersects the point $(-4, 6)$.

Thus, $f(g(6)) = f(-4) = 6$.

Would you like a more detailed explanation of any step?

Here are 5 related questions to deepen your understanding:

1. What is the significance of composite functions in real-life applications?
2. How would you evaluate $g(f(x))$ using the same graphs?
3. What happens if you input a value that is not on the graph?
4. Can composite functions be represented algebraically? How?
5. What properties of functions are important to understand when working with their graphs?

Tip: Always verify that you're reading the correct function by noting color, line style, or labels to avoid confusion!