To compare these numbers, we can rewrite them with positive exponents. The expression (a/b)^-n is equivalent to (b/a)^n. Therefore, (1/2)^-6 becomes 2^6, (1/4)^-3 becomes 4^3, (1/3)^-4 becomes 3^4, and (1/6)^-2 becomes 6^2. Calculating these values: 2^6 = 64, 4^3 = 64, 3^4 = 81, and 6^2 = 36. Comparing the results (64, 64, 81, 36), the largest number is 81, which corresponds to (1/3)^-4.