Option A: $(\frac{1}{2})^{-6} = 2^6 = 64$ Option B: $(\frac{1}{4})^{-3} = 4^3 = 64$ Option C: $(\frac{1}{3})^{-4} = 3^4 = 81$ Option D: $(\frac{1}{6})^{-2} = 6^2 = 36$

The largest value among the options is 81, which is from Option C: $(\frac{1}{3})^{-4}$