$1$ point$)$ Suppose that the characteristic equation for a differential equation is $(4)2(3)2=0($r$4)2($r$3)2=0.$

$($a$)$ Find such a differential equation, assuming it is homogeneous and has constant coefficients. Enter your answer using $,,,,$y$,$y$,$y$,$y$,$y$$ for the dependent variable and its derivatives.