Use the Brønsted–Lowry definition

A conjugate base is formed when a species loses one proton $\left(H^+\right)$.

Start with the given species

The species is hydroxide: $OH^-$

Remove one proton

If $OH^-$ loses $H^+$, we get: $OH^- \;\xrightarrow{-H^+}\; O^{2-}$

Check charge balance:

• Initial charge on $OH^- = -1$
• Removing $H^+$ increases negative charge by 1
• Final charge $= -2$

So the conjugate base is: $O^{2-}$

Check options

• A: $O_2$ — not formed by loss of one proton from $OH^-$
• B: $H_2O$ — this is the conjugate acid of $OH^-$, not the base
• C: $O^-$ — incorrect charge/species
• D: $O^{2-}$ — correct

Final answer

The conjugate base of $OH^-$ is: $\boxed{O^{2-}}$

Comparison with stored answer

Stored correct answer: D

My derived answer: D

They agree.