Answer
$\dfrac{y+2}{y-4}$
Work Step by Step
Subtracting the numerators and copying the denominator, the given expression, $
\dfrac{2y^2+3y}{y^2-7y+12}-\dfrac{y^2+4y+6}{y^2-7y+12}
,$ simplifies to
\begin{array}{l}\require{cancel}
\dfrac{2y^2+3y-(y^2+4y+6)}{y^2-7y+12}
\\\\=
\dfrac{2y^2+3y-y^2-4y-6}{y^2-7y+12}
\\\\=
\dfrac{y^2-y-6}{y^2-7y+12}
\\\\=
\dfrac{(y-3)(y+2)}{(y-4)(y-3)}
\\\\=
\dfrac{(\cancel{y-3})(y+2)}{(y-4)(\cancel{y-3})}
\\\\=
\dfrac{y+2}{y-4}
.\end{array}