In the complex K[Cr(H$_2$O)$_2$(C$_2$O$_4$)$_2$], chromium is coordinated to two water molecules (H$_2$O) and two oxalate ions (C$_2$O$_4^{2-}$). Oxalate is a bidentate ligand, meaning it coordinates through two oxygen atoms. Therefore, each oxalate ion contributes two coordination sites. Water molecules: 2 coordination sites Oxalate ions: 2 ions $\times$ 2 sites/ion = 4 coordination sites Total coordination number = 2 + 4 = 6.