Write 256 as $4^4$. Equality of powers of base 4 gives $8^x=4$. Now write both sides with base 2: $8^x=2^{3x}$ and $4=2^2$. Therefore $3x=2$, so $x=2/3$, option C. Check: $8^{2/3}=4$, which gives $4^4=256$ in the original equation.
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