Answer
$\dfrac{1}{5}y^2-8y+60$
Work Step by Step
Using $(a+b)(c+d)=ac+ad+bc+bd$ or the FOIL Method, the expression, $
\left( \dfrac{3}{5}y-6 \right)\left( \dfrac{1}{3}y-10 \right)
$, is equivalent to
\begin{array}{l}
\left( \dfrac{3}{5}y \right)\left( \dfrac{1}{3}y \right)+\left( \dfrac{3}{5}y \right)(-10)-6\left( \dfrac{1}{3}y \right)-6(-10)
\\\\=
\dfrac{1}{5}y^2-6y-2y+60
\\\\=
\dfrac{1}{5}y^2-8y+60
.\end{array}
