We are told that a system is linear and given inputs
$ \,x_1(t)=e^{2jt}\, $ yields $ \,y_1(t)=te^{-2jt}\, $
$ \,x_2(t)=e^{-2jt}\, $ yields $ \,y_2(t)=te^{2jt}\, $
The input
$ \,x(t)=cos(2t)\, $
can be rewritten as
$ \,x(t)=\frac{e^{2jt}+e^{-2jt}}{2}\, $
$ \,x(t)=\frac{1}{2}e^{2jt}+\frac{1}{2}e^{-2jt}\, $
