Step 1: Understanding coordination number.
The coordination number of a metal ion is the number of ligand atoms bonded to it. In \( [\text{Ni(C}_2\text{O}_4)_3]^{2-} \), each oxalate ion (\( \text{C}_2\text{O}_4^{2-} \)) is a bidentate ligand, meaning it bonds through two donor atoms. With three bidentate ligands, the coordination number of Ni is 6.
Step 2: Analysis of options.
(A) 3: This is incorrect; the coordination number is higher.
(B) 6: Correct — The coordination number of Ni in \( [\text{Ni(C}_2\text{O}_4)_3]^{2-} \) is 6 because each oxalate ion is bidentate.
(C) 4: This is incorrect; the complex contains three bidentate ligands, giving a coordination number of 6.
(D) 5: This is incorrect; a coordination number of 5 is not typical for this complex.
Step 3: Conclusion.
The correct answer is (B) because each oxalate ligand bonds with two donor atoms, leading to a coordination number of 6.