Coordination number of chromium(III) oxalate complex The coordination number refers to the number of binders that interact with the central metal ion. So, in the complex $\ce{[Cr(C2O4)3]^3-}$ chromium is bound to three oxalate ions.

Why its coordination number is considered 6? So, is it an incorrect definition of coordination number?

Can you help me?
This seems to be the case of "show, don't tell".

IUPAC's definition of coordination number (C.N.) which applies to inorganic complexes:


  In an inorganic coordination entity, the number of σ-bonds between ligands and the central atom. π-bonds are not considered in determining the coordination number.


Let's have a look at the one of the first determined structures of trioxalatochromate(III) inorganic salts [1]:


Figure 1. Crystal structure of $\ce{[Cr(C2O4)3]^3-}$ anion (ICSD-109607). Color scheme: $\color{#909090}{\Large\bullet}~\ce{C}$; $\color{#FF0D0D}{\Large\bullet}~\ce{O}$; $\color{#8A99C7}{\Large\bullet}~\ce{Cr}$.

Here, there are three oxalate $\ce{C2O4^2-}$ ligands arranged in distorted octahedral environment (depicted with semi-transparent coordination polyhedron).
Each oxalate is a bidentate chelating ligand, resulting in C.N. 6 of chromium center.

References


van Niekerk, J. N.; Schoening, F. R. L. The Crystal Structure of Ammonium Trioxalatochromate(III), $\ce{(NH4)3[Cr(C2O4)3].2H2O}.$ Acta Cryst 1952, 5 (4), 499–505. DOI: 10.1107/S0365110X52001428.