Determine a cartesian equation for the curve given in parametric form

X(t)=2e^2t
y(t)=3e^-t

Note that y = 3e^(-t)
==> e^t = 3/y.

Therefore,
x = 2e^(2t)
...= 2(e^t)^2
...= 2(3/y)^2
...= 18/y^2.

That is, xy^2 = 18 is the cartesian equation of the curve.

I hope this helps!