Let's analyze the graph of $h(x)$ and match the values from the curve to fill in the table. The values of $x$ given in the table are $-2, -1, 0, 1, 2, 3$, and we'll find their corresponding $h(x)$ values using the graph.

Here’s the approach:

1. Find $h(x)$ at $x = -2$: From the graph, it looks like the value is 0. This is already filled in the table.

2. Find $h(x)$ at $x = -1$: From the graph, the value of $h(x)$ when $x = -1$ is 12. This is also filled in.

3. Find $h(x)$ at $x = 0$: The value when $x = 0$ is also 12, and this is already filled in as well.

4. Find $h(x)$ at $x = 1$: When $x = 1$, the graph shows the value of $h(x) = 4$.

5. Find $h(x)$ at $x = 2$: At $x = 2$, the value of $h(x)$ is 0.

6. Find $h(x)$ at $x = 3$: Finally, at $x = 3$, $h(x)$ reaches 8.

Completed Table: