Here's the problem:
$ \,Input \rightarrow SYSTEM \rightarrow Output $
- $ \,e^{2jt} \rightarrow SYSTEM \rightarrow te^{-2jt} $
- $ \,e^{-2jt} \rightarrow SYSTEM \rightarrow te^{2jt} $
From the information given above, it seems like the system takes an input $ \,x(t) $ and transforms in into an output $ \,y(t) = tx(-t) $
For an input $ \,x(t) = cos(2t) $
- $ \,cos(2t) \rightarrow SYSTEM \rightarrow tcos(-2t) $
Thus, $ \,y(t) = tcos(-2t) $
