Chapter 1, Equations and Inequalities - 1.7 Solve Absolute Value Equations and Inequalities - 1.7 Exercises - Skill Practice - Page 55: 31

$$y=-20\quad \mathrm{or}\quad \:y=4$$

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: $$0.5y+4=-6\quad \mathrm{or}\quad \:0.5y+4=6 \\ y=-20\quad \mathrm{or}\quad \:y=4$$