Step 1: Understanding the Concept:
Coordination number is the number of donor atoms directly bonded to the central metal ion, not the number of ligand molecules.
Step 2: Key Point:
Ethylenediamine (en), \(\text{NH}_2\text{CH}_2\text{CH}_2\text{NH}_2\), is a bidentate ligand. It binds the metal through two nitrogen atoms.
Step 3: Detailed Explanation:
In \([\text{Co(en)}_3]^{3+}\) there are 3 en ligands, each attached through 2 donor atoms:
\[ \text{Coordination number} = 3 \times 2 = 6 \]
The geometry is octahedral.
Step 4: Why the other options are wrong.
The value 2 or 4 would apply to a complex with fewer donor atoms, such as \([\text{Ag(NH}_3)_2]^+\) or \([\text{Ni(CN)}_4]^{2-}\). The value 8 is not found here since only six donor atoms are present.
Final Answer:
The coordination number is 6, option (C).
\[ \boxed{6} \]