find series and shunt components of matching network
The statement in the question tells you \$ Z_{out}^{*} = Z_{in} \$ where \$ Z_{in} = X_{2} + R_{1}X_{1}/(R_{1}+X_{1})\$.

You also know \$ X_{1} \$ and \$ X_{2}  \$ are only imaginary, therefore you can split the equation for \$ Z_{in} \$ in real and imaginary parts to get 2 equations, repectivly to \$ X_{1} \$ and \$ X_{2}  \$.
Now you can solve the equation system and you will get the correct values.