Answer
$x-14\sqrt[]{x-6}+43$
Work Step by Step
Using $(a+b)^2=a^2+2ab+b^2$ or the square of a binomial, then,
\begin{array}{l}
\left( \sqrt[]{x-6}-7 \right)^2
\\=
(\sqrt[]{x-6})^2+2(\sqrt[]{x-6})(-7)+(-7)^2
\\=
x-6-14\sqrt[]{x-6}+49
\\=
x-14\sqrt[]{x-6}+43
.\end{array}