To find $f(x) = 2$ for the given function, we need to determine the $x$-values where the function's output $y$ is equal to 2.

1. Identify the points on the graph where $y = 2$: Look for the points where the function intersects the horizontal line $y = 2$.

2. Examine the graph: The function appears to be a V-shaped graph, which resembles an absolute value function. The graph has two segments:

   • A left segment sloping upward from left to right.
   • A right segment sloping upward from left to right.

3. Find the intersection points:

   • On the left side of the graph, trace along the line where $y = 2$ until you find where it intersects with the graph. This occurs at $x = -6$.
   • On the right side of the graph, trace where $y = 2$ intersects the function. This occurs at $x = 4$.

Thus, the function $f(x) = 2$ when $x = -6$ and $x = 4$.

Final Answer:

The solutions are: $x = -6 \quad \text{and} \quad x = 4$

Would you like a deeper explanation of this process or have any other questions?

Here are some related questions you might find helpful:

1. How do you determine the equation of an absolute value function from a graph?
2. What is the general form of an absolute value function?
3. How can you find the vertex of a V-shaped graph?
4. How do you determine the slopes of each segment in a piecewise linear function?
5. What are some other examples of piecewise functions?

Tip: When analyzing graphs, identifying symmetry and slopes can often simplify finding specific values of $x$ or $y$ in piecewise functions.