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To write the net ionic equation, we need to first write the balanced molecular equation and then identify the spectator ions to eliminate from the equation.
The balanced molecular equation is:
2 FeCl3(aq) + 3 Li2CO3(aq) --> Fe2(CO3)3(s) + 6 LiCl(aq)
To write the net ionic equation, we need to identify the ions that are actually involved in the reaction and eliminate the spectator ions (ions that do not participate in the reaction and remain unchanged throughout the reaction).