Carbon (C) has an atomic number of 6, which means it has 6 protons and, in its neutral state, 6 electrons.
Step 2: Determine the Electron Configuration of Neutral Carbon
The electron configuration of a neutral carbon atom is:
\[ 1s^2 2s^2 2p^2 \]
Step 3: Determine the Electron Configuration of the $\mathrm{C}^{4-}$ Ion
The $\mathrm{C}^{4-}$ ion has gained 4 additional electrons compared to the neutral carbon atom. Therefore, the total number of electrons in $\mathrm{C}^{4-}$ is:
\[ 6 + 4 = 10 \]
Step 4: Write the Electron Configuration for $\mathrm{C}^{4-}$
With 10 electrons, the electron configuration for $\mathrm{C}^{4-}$ is:
\[ 1s^2 2s^2 2p^6 \]