\[\left( y^{3} \cdot y \right)^{3} \cdot \left( y^{3} \cdot y \right)^{2} =\]
\[= \left( y^{3 + 1} \right)^{3} \cdot \left( y^{3 + 1} \right)^{2} =\]
\[= \left( y^{4} \right)^{3} \cdot \left( y^{4} \right)^{2} =\]
\[= y^{12} \cdot y^{8} = y^{12 + 8} = y^{20}.\]