Four reactions of the butene isomers are carried out: (I) (Z)-but-2-ene with OsO4 followed by NaHSO3; (II) (E)-but-2-ene with m-CPBA followed by…

Treat each reaction by its stereochemistry. (I) $\mathrm{OsO_4}$ gives syn addition of two OH groups; syn addition to the $Z$ alkene gives the $meso$ butane-2,3-diol. (II) The epoxide from $m$-CPBA retains the alkene geometry, and acid-catalysed ring opening by water is anti (backside attack); net anti dihydroxylation of the $E$ alkene gives the $meso$ diol. (III) Bromination is anti addition; anti addition to the $Z$ alkene gives the $(2R,3R)/(2S,3S)$ pair, i.e. a racemic dibromide. (IV) Cold alkaline permanganate is syn addition; syn addition to the $E$ alkene gives the racemic $(2R,3R)/(2S,3S)$ diol. Rule: syn on $Z$ or anti on $E$ gives $meso$; syn on $E$ or anti on $Z$ gives racemate. Hence only I and II give $meso$ products.