Answer
$y-y^{7/6}$
Work Step by Step
Using the Distributive Property and the laws of exponents, then,
\begin{array}{l}
y^{1/2}(y^{1/2}-y^{2/3})
\\\\=
y^{\frac{1}{2}+\frac{1}{2}}-y^{\frac{1}{2}+\frac{2}{3}}
\\\\=
y^{\frac{2}{2}}-y^{\frac{3}{6}+\frac{4}{6}}
\\\\=
y-y^{7/6}
.\end{array}