#### Answer

{$22$}

#### Work Step by Step

Step 1: $\log_{8} (3x-2)=2$
Step 2: Transforming the logarithmic form into its corresponding exponential statement, $3x-2=8^{2}$
Step 3: $3x-2=64$
Step 4: $3x-2+2=64+2$
Step 5: $3x=66$
Step 6: $x=\frac{66}{3}=22$
Step 7: Therefore, the solution set is {$22$}.