Another way to solve this is to mentally track what happens to just one face-defining feature, the relationship between the two phenyl groups, as each addition occurs, rather than quoting the general cis/trans-syn/anti rule from memory.
- cis-stilbene: in the starting alkene the two phenyl groups sit on the same side of the double bond.
- trans-stilbene: in the starting alkene the two phenyl groups sit on opposite sides of the double bond.
- $OsO_4$/$NMO$ (syn addition): both new $C-OH$ bonds form on the same face of the flat alkene. Starting from cis-stilbene, adding both $OH$ groups to one face keeps the two $Ph$ groups in a mirror-related arrangement in the product, which is exactly the internal-mirror-plane condition that defines a meso compound.
- $I_2$/$AgOAc$ then $NaOH$/$H_2O$ (net anti addition, Prevost): the two new $C-O$ bonds end up on opposite faces of what was the flat alkene. Starting from trans-stilbene, where the phenyls were already on opposite sides, adding the two oxygens to opposite faces again reconstructs the mirror-related, meso arrangement in the product.
- The two "mismatched" combinations, cis-alkene with anti addition, and trans-alkene with syn addition, each end up putting the two stereocenters into a same-handed ($R,R$ or $S,S$) relationship instead, giving the chiral, optically active $d,l$ diol rather than the meso diol.
Checking the four options against this: (A) is cis-stilbene with syn ($OsO_4$) addition, a matched pair giving meso. (B) is trans-stilbene with syn addition, mismatched, giving $d,l$. (C) is cis-stilbene with anti (Prevost) addition, mismatched, giving $d,l$. (D) is trans-stilbene with anti (Prevost) addition, a matched pair giving meso.
Let's summarize:
- Meso hydrobenzoin needs the alkene geometry and the addition face-selectivity to be "matched" in the sense described above.
- That matching happens for cis-stilbene/syn and for trans-stilbene/anti, which are options (A) and (D).
The correct options are (A) and (D).