Answer
{$\frac{8}{9}$}
Work Step by Step
Step 1: $8^{3x-2}=4$
Step 2: $(2^{3})^{3x-2}=2^{2}$
Step 3: $2^{9x-6}=2^{2}$
Step 4: $9x-6=2$
Step 5: $9x=2+6$
Step 6: $9x=8$
Step 7: $x=\frac{8}{9}$
Therefore, the solution set is {$\frac{8}{9}$}.