1. The problem is to simplify the expression $$\sqrt[4]{64m^{6}n^{12}}$$. 2. Start by expressing each part inside the fourth root separately: $$\sqrt[4]{64} \times \sqrt[4]{m^{6}} \times \sqrt[4]{n^{12}}$$. 3. Simplify $$\sqrt[4]{64}$$: since $$64 = 2^{6}$$, $$\sqrt[4]{64} = 64^{1/4} = (2^{6})^{1/4} = 2^{6/4} = 2^{3/2} = 2^{1} \times 2^{1/2} = 2\sqrt{2}$$. 4. Simplify $$\sqrt[4]{m^{6}} = m^{6/4} = m^{3/2} = m^{1} \times m^{1/2} = m\sqrt{m}$$. 5. Simplify $$\sqrt[4]{n^{12}} = n^{12/4} = n^{3}$$. 6. Now multiply all simplified parts: $$2\sqrt{2} \times m\sqrt{m} \times n^{3} = 2mn^{3} \sqrt{2m}$$. 7. Therefore, the simplified form is $$\boxed{2mn^{3}\sqrt{2m}}$$.