To solve this equation, we can first rewrite it as:

6^(1-4x) = 216

Now, we know that 216 can be written as 6^3, so our equation becomes:

6^(1-4x) = 6^3

Since the bases are the same on both sides of the equation, we can set the exponents equal to each other:

1-4x = 3

Now we solve for x:

1 - 4x = 3
-4x = 2
x = -0.5

Therefore, the solution to the equation 6^(1-4x) = 216 is x = -0.5.