The coordination number of a complex refers to the number of ligands in this case, water molecules directly bonded to the central metal ion in this case, Ce3+ . In the given complex [Ce H2O 9]3+, there are 9 water molecules bonded to the Ce3+ ion. However, you mentioned assuming an octahedral geometry for the complex.An octahedral geometry can only accommodate 6 ligands around the central metal ion. Therefore, if we assume an octahedral geometry, the coordination number for the [Ce H2O 9]3+ ion would be 6, not 9. This assumption would mean that the complex is not accurately represented by the given formula, and there might be some error in the information provided.