The problem you're looking at asks about two graphed functions, $f(x)$ and $g(x)$, which are plotted in blue and red, respectively. We need to determine which statement regarding these functions is true based on the graph.

Let's analyze the options step by step:

1. $f(4) = g(4)$: This means at $x = 4$, the values of both $f(x)$ and $g(x)$ must be equal. Looking at the graph:

   • The value of $f(4)$ appears to be around $-12$.
   • The value of $g(4)$ appears to be around $6$. Since these values are not equal, this option is false.

2. $f(-2) = g(-2)$: This means at $x = -2$, the values of both functions must be the same.

   • The value of $f(-2)$ appears to be about $6$.
   • The value of $g(-2)$ is also around $6$. Since these values are equal, this statement is true.

3. $f(2) = g(-2)$: This compares $f(2)$ and $g(-2)$.

   • The value of $f(2)$ seems to be around $-6$.
   • The value of $g(-2)$ is $6$, as noted earlier. These values are not equal, so this option is false.

4. $f(4) = g(-2)$: This compares $f(4)$ and $g(-2)$.

   • $f(4)$ is around $-12$.
   • $g(-2)$ is $6$. These values are not equal, so this option is false.

The correct answer is $f(-2) = g(-2)$, or the second option.

Would you like more details or have any questions? Here are some related questions:

1. How do you find the value of a function at a specific point from a graph?
2. How can we determine if two functions are equal at a particular $x$-value?
3. What are the key characteristics to observe in a graph to identify intersections?
4. How do linear functions differ in slope and y-intercept?
5. How can we use function notation effectively in evaluating graph-based problems?

Tip: Always check the points of intersection in a graph as they often provide answers where two functions are equal at specific values.