Step 1: Understanding the Concept:
Coordination isomerism occurs in salts where both the cation and the anion are complex ions, and there is an exchange of ligands between the two metal centers.
Step 2: Detailed Explanation:
1. In the first complex $[Co(NH_3)_6][Cr(CN)_6]$, $NH_3$ is bonded to $Co$ and $CN^-$ is bonded to $Cr$.
2. In the second complex $[Cr(NH_3)_6][Co(CN)_6]$, the ligands have swapped centers: $NH_3$ is now bonded to $Cr$ and $CN^-$ is bonded to $Co$.
3. This swap of ligands between two metal coordination spheres is the definition of coordination isomerism.
Step 3: Final Answer:
These are examples of coordination isomerism.