Answer
$(NH_4)_2CO_3$, $H2S_{(aq.)}$ and $NaOH$ form precipitates with the two ions, so they will not work.
Neither $HNO_3$ nor $NH3_{(aq.)}$ will work because neither
ion would precipitate.
$HCl_{(aq.)}$ will work because $AgCl$ is not water soluble and $CuCl_2$ is.
Work Step by Step
$(NH_4)_2CO_3$, $H2S_{(aq.)}$ and $NaOH$ form precipitates with the two ions, so they will not work.
Neither $HNO_3$ nor $NH3_{(aq.)}$ will work because neither
ion would precipitate.
$HCl_{(aq.)}$ will work because $AgCl$ is not water soluble and $CuCl_2$ is.
