Given:

\(\displaystyle{2}\sqrt{{{6}}}{\left({8}-{4}\sqrt{{{3}}}\right)}\)

open the bracket then multiply

\(\displaystyle={2}\times{8}\sqrt{{{6}}}-{2}\times{4}\sqrt{{{6}}}\times\sqrt{{{3}}}\)

\(\displaystyle={16}\sqrt{{{6}}}-{8}\sqrt{{{6}\times{3}}}\)

\(\displaystyle={16}\sqrt{{{6}}}-{8}\sqrt{{{3}\times{3}\times{2}}}\)

square root of \(\displaystyle{3}\times{3}\) is 3 therefore

\(\displaystyle={16}\sqrt{{{6}}}-{3}\times{8}\sqrt{{{2}}}\)

\(\displaystyle={16}\sqrt{{{6}}}-{24}\sqrt{{{2}}}\) - Answer

\(\displaystyle{2}\sqrt{{{6}}}{\left({8}-{4}\sqrt{{{3}}}\right)}\)

open the bracket then multiply

\(\displaystyle={2}\times{8}\sqrt{{{6}}}-{2}\times{4}\sqrt{{{6}}}\times\sqrt{{{3}}}\)

\(\displaystyle={16}\sqrt{{{6}}}-{8}\sqrt{{{6}\times{3}}}\)

\(\displaystyle={16}\sqrt{{{6}}}-{8}\sqrt{{{3}\times{3}\times{2}}}\)

square root of \(\displaystyle{3}\times{3}\) is 3 therefore

\(\displaystyle={16}\sqrt{{{6}}}-{3}\times{8}\sqrt{{{2}}}\)

\(\displaystyle={16}\sqrt{{{6}}}-{24}\sqrt{{{2}}}\) - Answer