\[2\sqrt{8} + 3\sqrt{32} - \frac{1}{4}\sqrt{128} =\]
\[= 2\sqrt{4 \cdot 2} + 3\sqrt{16 \cdot 2} - \frac{1}{4}\sqrt{64 \cdot 2} =\]
\[= 2 \cdot 2\sqrt{2} + 3 \cdot 4\sqrt{2} - \frac{1}{4} \cdot 8\sqrt{2} =\]
\[= 4\sqrt{2} + 12\sqrt{2} - 2\sqrt{2} = 14\sqrt{2}.\]