1. Find total number of electrons in $O_2^{2-}$

Each oxygen atom has $8$ electrons. So, neutral $O_2$ has: $8+8=16$ For $O_2^{2-}$, add $2$ more electrons: $16+2=18$

So, $O_2^{2-}$ has 18 electrons.

2. Write the MO configuration for $O_2^{2-}$

For oxygen and heavier diatomic molecules, the molecular orbital order is: $\sigma_{1s},\ \sigma_{1s}^*,\ \sigma_{2s},\ \sigma_{2s}^*,\ \sigma_{2p_z},\ \pi_{2p_x}=\pi_{2p_y},\ \pi_{2p_x}^*=\pi_{2p_y}^*,\ \sigma_{2p_z}^*$

Filling $18$ electrons: $\left(\sigma_{1s}\right)^2\left(\sigma_{1s}^*\right)^2\left(\sigma_{2s}\right)^2\left(\sigma_{2s}^*\right)^2\left(\sigma_{2p_z}\right)^2\left(\pi_{2p_x}\right)^2\left(\pi_{2p_y}\right)^2\left(\pi_{2p_x}^*\right)^2\left(\pi_{2p_y}^*\right)^2$

3. Identify all bonding molecular orbitals

Bonding MOs occupied here are:

• $\sigma_{1s}$ : $2$ electrons
• $\sigma_{2s}$ : $2$ electrons
• $\sigma_{2p_z}$ : $2$ electrons
• $\pi_{2p_x}$ : $2$ electrons
• $\pi_{2p_y}$ : $2$ electrons

Total electrons in all bonding molecular orbitals: $2+2+2+2+2=10$

4. Final answer

The total number of electrons in all bonding molecular orbitals of $O_2^{2-}$ is: $\boxed{10}$

5. Comparison with stored answer

Stored correct answer = $10$

Our derived answer = $10$

So, the answer agrees with the stored correct answer.