Let's talk about the conjugate bases:
A conjugate base is the base member, X-, of a pair of compounds that transform into each other by gaining or losing a proton. The conjugate base is able to gain or absorb a proton in a chemical reaction. The conjugate acid donates the proton or hydrogen in the reaction.
In this question, we're asked to find the conjugate base of the ion:
As we can notice, the ion (CO3)2- would not have a conjugate base, as it cannot lose any more hydrogen atoms. A correct statement could be that it is a conjugate base of a hydrogencarbonate.
Therefore, (CO3)2- ion has not a conjugate base because it actually is a conjugate base of a hydrogencarbonate.