The given equation is
[tex]|26-4c|=-2[/tex]Remember that an absolute value equation is rewritten as two other equations
[tex]\begin{gathered} 26-4c=-2 \\ 26-4c=-(-2) \end{gathered}[/tex]Let's solve both equations
[tex]26-4c=-2\rightarrow-4c=-2-26\rightarrow-4c=-28\rightarrow c=\frac{-28}{-4}=7[/tex][tex]26-4c=-(-2)\rightarrow26-4c=2\rightarrow-4c=2-26\rightarrow c=\frac{-24}{-4}=6[/tex]