\sqrt{\frac{32.\sqrt{6}}{\sqrt{12}}}

$$\sqrt{\frac{32 \cdot \sqrt{6}}{\sqrt{12}}} = \sqrt{\frac{32 \cdot \sqrt{6}}{\sqrt{2 \cdot 6}}} = \sqrt{\frac{32 \cdot \sqrt{6}}{\sqrt{2} \cdot \sqrt{6}}} = \sqrt{\frac{32}{\sqrt{2}}} = \sqrt{\frac{32 \cdot \sqrt{2}}{2}} = \sqrt{16 \cdot \sqrt{2}} = 4 \sqrt[4]{2}$$

Ответ: $$4 \sqrt[4]{2}$$