Determining whether something is an acid, base, or amphoteric
An amphoteric substance can act both as an acid and a base. That is, an amphoteric substance can donate protons and also accept protons.

$\ce{CO3^{-2}}$ does not have any protons so it cannot act as an acid. It is the conjugate base of $\ce{HCO3^{-}}$.

$\ce{HPO4^-{2}}$ is the conjugate base of $\ce{H2PO4^{-}}$. It can accept a proton to go back to $\ce{H2PO4^{-}}$ or it can donate a proton to become $\ce{PO4^{-3}}$. Thus, it is amphoteric.

$\ce{H3O^{+}}$ is the conjugate acid of $\ce{H2O}$. It can donate a proton to go back to $\ce{H2O}$ but it cannot accept any other protons. Thus, it not amphoteric.

$\ce{NH4^{+}}$ is similar to $\ce{H2O}$. In this case it is the conjugate acid of $\ce{NH3}$. As such it can donate a proton to go back to $\ce{NH3}$ but it cannot accept any protons. It is not amphoteric.

So, out of your list only $\ce{HPO4^-{2}}$ is apmhoteric.