We start with the expression \((54y)^{\frac{2}{3}}\). To simplify this, we first calculate the cube root of \(54y\) and then square the result.
Step 2: Simplification
The expression simplifies to approximately \(14.2866y^{\frac{2}{3}}\). This can be expressed as:
\[
(54y)^{\frac{2}{3}} \approx 14.2866y^{\frac{2}{3}}
\]
Final Answer
The simplified expression is:
\[
\boxed{14.2866y^{\frac{2}{3}}}
\]