6 - 4 3 + 16 - 8 3 is equal to = ?

Answer: Option B

$$\begin{array}{rl}& \sqrt{6-4\sqrt{3}+\sqrt{16-8\sqrt{3}}}\\ & =\sqrt{6-4\sqrt{3}+\sqrt{12+4-8\sqrt{3}}}\\ & =\sqrt{6-4\sqrt{3}+\sqrt{{\left(2\sqrt{3}\right)}^2+{\left(2\right)}^2-2\times 2\sqrt{3}\times 2}}\\ & =\sqrt{6-4\sqrt{3}+\sqrt{{\left(2\sqrt{3}-2\right)}^2}}\\ & =\sqrt{6-4\sqrt{3}+2\sqrt{3}-2}\\ & =\sqrt{{\left(\sqrt{3}\right)}^2+{\left(1\right)}^2-2\times \sqrt{3}\times 1}\\ & =\sqrt{{\left(\sqrt{3}-1\right)}^2}\\ & =\sqrt{3}-1\end{array}$$