You may have correctly subtracted 7 from both sides to get $\displaystyle{\left|{4}{y}-{2}\right|}={30}\usepackage{cmbright}\Huge\$ , but then solved only $\displaystyle{4}{y}-{2}={30}\usepackage{cmbright}\Huge\$ . If $\displaystyle{\left|{X}\right|}={30}\usepackage{cmbright}\Huge\$ , then $\displaystyle{X}={30}\usepackage{cmbright}\Huge\$ or $\displaystyle{X}=-{30}\usepackage{cmbright}\Huge\$ . In this problem, X is replaced by $\displaystyle{4}{y}-{2}\usepackage{cmbright}\Huge\$ . So you should be solving two equations, $\displaystyle{4}{y}-{2}={30}\usepackage{cmbright}\Huge\$ and $\displaystyle{4}{y}-{2}=-{30}\usepackage{cmbright}\Huge\$ , but you forgot one of them.