Step 1: Write the formula.
Formal charge is $\text{FC} = V - N - \dfrac{B}{2}$, where $V$ is valence electrons, $N$ is lone pair electrons, and $B$ is the shared bonding electrons.
Step 2: Draw the carbonate ion.
In $\text{CO}_3^{2-}$ the central carbon joins three oxygens, one by a double bond and two by single bonds.
Step 3: Find $V$.
Carbon is in group 14, so it has $4$ valence electrons. So $V = 4$.
Step 4: Find $N$.
Carbon uses all its electrons in bonding and keeps no lone pair, so $N = 0$.
Step 5: Find $B$ and compute.
Carbon makes four bonds in total (one double and two single), so it shares $8$ bonding electrons, giving $B = 8$. Now $\text{FC} = 4 - 0 - \dfrac{8}{2} = 4 - 4 = 0$.
Step 6: Final choice.
The formal charge on carbon is zero, which is option 4.
\[ \boxed{\text{zero}} \]