Transformation A gives the cis-exo-2,3-diol (both OH on the exo face). Cold alkaline KMnO₄ is a syn dihydroxylation and attacks norbornene from the less hindered exo face.
Transformation B gives the cis-endo diol. Under Woodward conditions (I₂, PhCO₂Ag with H₂O, then aq. NaOH), iodine adds to the exo face. Neighbouring-group participation by the benzoate through a dioxolanium ion places oxygen on the endo face, water traps it as the cis-hydroxy benzoate, and NaOH hydrolyses the ester to the cis-endo diol.
Why the others fail: (a) Prévost conditions without water give a trans diol; (c) puts a trans diol for A and OsO₄ gives the exo, not endo, diol for B; (d) m-CPBA then NaOH gives a trans diol for A. Answer: (b).
Study loop for Reagents, Reaction Mechanisms & Named Reactions