To solve the equation 2x^2 - 6log(2x) = -8, we need to use properties of logarithms to simplify the equation.

First, we can use the property that log(a) - log(b) = log(a/b) to rewrite the equation as:
log((2x^2)/(2x^6)) = -8

Next, simplify the equation further by dividing out the common factor in the logarithm:
log(x) = -8

Now, we can rewrite the equation in exponential form to solve for x:
10^(-8) = x

Therefore, the solution to the equation 2x^2 - 6log(2x) = -8 is x = 10^(-8).