express 2y/3+2y-6/15

$$\begin{array}{lcl}
\mbox{express } \frac{2y}{3}+2y-\frac{6}{15} \mbox{ (in a simpler form?)}\\
\frac{2y}{3}+2y-\frac{6}{15}\\
\frac{2y}{3}+2y*1-\frac{6}{15}\\
\frac{2y}{3}+2y*\frac{3}{3}-\frac{6}{15}\\
\frac{2y}{3}+\frac{6y}{3}-\frac{6}{15}\\
\frac{2y+6y}{3}-\frac{6}{15}\\
\frac{8y}{3}-\frac{6}{15}\\
\frac{8y}{3}*1-\frac{6}{15}\\
\frac{8y}{3}*\frac{5}{5}-\frac{6}{15}\\
\frac{40y}{15}-\frac{6}{15}\\
\frac{40y-6}{15}
\end{array}$$

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