The given expression is
[tex](x+6)^2-16=0[/tex]First, we add 16 on each side
[tex]\begin{gathered} (x+6)^2-16+16=16 \\ (x+6)^2=16 \end{gathered}[/tex]Then, we apply a square root on each side
[tex]\begin{gathered} \sqrt[]{(x+6)^2}=\sqrt[]{16} \\ x+6=\pm4 \end{gathered}[/tex]Now, we subtract 6 from each side
[tex]\begin{gathered} x+6-6=\pm4-6 \\ x_1=4-6=-2 \\ x_2=-4-6=-10 \end{gathered}[/tex]Therefore, the lesser solution is -10 and the greater solution is -2.