From the uploaded image, the task is to determine the limit of $H(x)$ as $x \to -2$ using the given graph.

Step-by-step solution:

1. Identify the behavior of $H(x)$ as $x \to -2$:

   • Locate $x = -2$ on the graph.
   • Analyze the y-values of $H(x)$ as $x$ approaches $-2$ from the left ($x \to -2^-$) and from the right ($x \to -2^+$).

2. From the graph:

   • As $x \to -2^-$ (approaching $-2$ from the left), the y-values approach 6.
   • As $x \to -2^+$ (approaching $-2$ from the right), the y-values also approach 6.

3. Conclusion:

   • Since the y-values from both sides approach the same value, the limit exists and is equal to $6$.

Final Answer:

• Select option A: $\lim_{x \to -2} H(x) = 6$.

Let me know if you'd like further clarification or a detailed explanation of this process!