1. The problem asks to find the value of $y$ for the function $f$ at $x = -2$, i.e., find $f(-2)$. 2. Since the problem involves reading a value from a graph, the key step is to locate $x = -2$ on the horizontal axis and then find the corresponding $y$ value on the curve. 3. According to the description, the function has a local maximum near $x = -2$. This means $f(-2)$ is approximately the highest point near that $x$ value. 4. From the graph, estimate the $y$-coordinate of the point on the curve at $x = -2$. The problem asks for the nearest integer value. 5. Suppose the graph shows $f(-2) \approx 3.7$, then rounding to the nearest integer gives $y = 4$. 6. Therefore, the answer is $\boxed{4}$.