Answer: (D) \(4\sqrt{2}\)
Equilateral triangles are similar, so the ratio of their areas equals the ratio of the squares of their sides:
\[\frac{AB^2}{DE^2} = \frac{1}{2}\] \[DE^2 = 2 \times 16 = 32\] \[DE = 4\sqrt{2}\](A) \(2\sqrt{2}\) would make DEF smaller than ABC, which contradicts the ratio 1 : 2.