Chapter 1, Equations and Inequalities - 1.7 Solve Absolute Value Equations and Inequalities - 1.7 Exercises - Skill Practice - Page 55: 14

$$h=0\quad \mathrm{or}\quad \:h=8$$

Since the value inside the absolute value can be positive or negative and get the same number, we must consider both options. Doing this, we find: $$\left|h-4\right|=4 \\ h-4=-4\quad \mathrm{or}\quad \:h-4=4\\ h=0\quad \mathrm{or}\quad \:h=8$$