[2 * 4^x]^{1/3} = 8^{1 - x} <-- Cube both sides

2 * 4^x = [8^{1 - x}]^3

2 * 4^x = 8^{3(1 - x)}

2 * [2^2]^x = [2^3]^{3(1 - x)}

2*2^{2x} = 2^{9(1 - x)}

2^{2x + 1} = 2^{9(1 - x)}

Equating exponents:

2x + 1 = 9(1 - x)

2x + 1 = 9 - 9x

11x = 8

x = 8/11

So yes, you are correct!

-Dan