Subtract 4 from all parts: $\displaystyle-{2}-{4}\le-{2}{k}+{4}-{4}\le{6}-{4}\usepackage{cmbright}\Huge\$

Simplify to: $\displaystyle-{6}\le-{2}{k}\le{2}\usepackage{cmbright}\Huge\$

Divide all parts by $\displaystyle-{2}\usepackage{cmbright}\Huge\$ , and reverse the inequality signs.

$\displaystyle\frac{{-{6}}}{{-{{2}}}}\ge\frac{{-{2}{k}}}{{-{{2}}}}\ge\frac{{{2}}}{{-{2}}}\usepackage{cmbright}\Huge\$ , so $\displaystyle{3}\geq{k}\geq-{1}\usepackage{cmbright}\Huge\$ or $\displaystyle-{1}\le{k}\le{3}\usepackage{cmbright}\Huge\$