Answer
$12y^2-\dfrac{3}{2}y+\dfrac{1}{24}$
Work Step by Step
Using the FOIL Method, $(a+b)(c+d)=ac+ad+bc+bd$, the given expression simplifies to
\begin{align*}
&
\left( 4y-\dfrac{1}{3} \right)\left( 3y-\dfrac{1}{8} \right)
\\\\&=
12y^2-\dfrac{1}{2}y-y+\dfrac{1}{24}
\\\\&=
12y^2-\dfrac{1}{2}y-\dfrac{2}{2}y+\dfrac{1}{24}
\\\\&=
12y^2-\dfrac{3}{2}y+\dfrac{1}{24}
.\end{align*}
