The problem is to solve the inequality $2 < h - 6$ and graph the solution on a number line.

1. Problem Description

The problem is to solve the inequality $2 < h - 6$ and graph the solution on a number line.

2. Solution Steps

First, we need to isolate $h$ in the inequality $2 < h - 6$. To do this, we add 6 to both sides of the inequality.

$2 + 6 < h - 6 + 6$

$8 < h$

This is the same as $h > 8$.

Now we need to graph $h > 8$ on a number line. Since $h$ is strictly greater than 8, we use an open circle at 8 to indicate that 8 is not included in the solution. Then, we draw an arrow to the right, indicating that all values greater than 8 are part of the solution.

3. Final Answer

The solution to the inequality is $h > 8$. On the number line, there should be an open circle at 8 and an arrow extending to the right.