Step 1: Understand primary and secondary valency.
Primary valency corresponds to oxidation state of metal, while secondary valency corresponds to coordination number (number of ligands directly attached to metal).
Step 2: Determine oxidation state of Cr.
In CrCl\(_3\cdot 6H_2O\), chromium is in +3 oxidation state because 3 chloride ions balance it:
\[
\text{Primary valency} = 3
\]
Step 3: Identify coordination sphere.
6 water molecules act as ligands in coordination sphere, so total ligands attached to Cr = 6.
Step 4: Determine secondary valency.
Secondary valency = number of ligands directly attached = 6.
Step 5: Determine coordination number.
Coordination number = 6 (octahedral complex).
Step 6: Final conclusion.
\[
x = 3,\quad y = 6,\quad z = 6
\]
\[
\boxed{(3,6,6)}
\]