Answer
See work below.
Work Step by Step
To find out a procedure for separation of these ions, we need to find out their difference based on the classifications of cations. $Ag^{+}$ is on Group 1, as $AgCl$ is an insoluble chloride. Meanwhile, $Mn^{2+}$ is on Group 3, as $MnS$ is a base-insoluble sulfide. However, by being on Group 3, it also means that $Mn^{2+}$ can form a soluble chloride. Thus, we can setup the following procedure:
From the original solution, we add an abundant amount of $HCl$ into the solution. As a result, $AgCl$ precipitates. Then, by using filtration, solid silver chloride stays on filter paper, while the filtrate consists largely of $Mn^{2+}$.
