Calculate all four second-order partial derivatives of $\displaystyle f(x,y) = \left(2x+4y\right)e^{y}$.

$f_{xx} \, (x,y) =$

$f_{xy} \, (x,y) =$

$f_{yx} \, (x,y) =$

$f_{yy} \, (x,y) =$