Answer
$-2e^{2s}$
Work Step by Step
$Jacobian =\begin{vmatrix} \dfrac{\partial x}{\partial s}&\dfrac{\partial x}{\partial t}\\\dfrac{\partial y}{\partial s}&\dfrac{\partial y}{\partial t}\end{vmatrix}$
Now,
$Jacobian=\begin{vmatrix} e^{s+t}&e^{s+t}\\e^{s-t}&-e^{s-t}\end{vmatrix}=-2 e^{s+t}e^{s-t}=-2 e^{s+t+s-t}=-2e^{2s}$
