Reagent used to convert allyl alcohol to acrolein is

The target transformation is $$CH_2=CH-CH_2OH \;\longrightarrow\; CH_2=CH-CHO$$, i.e. selective oxidation of an allylic primary alcohol to an aldehyde while leaving the C=C bond untouched.

Activated $$MnO_2$$ (manganese(IV) oxide) is a well-known reagent that
• oxidises allylic and benzylic alcohols to the corresponding carbonyl compounds,
• does not cleave or further oxidise the isolated C=C bond, and
• normally stops at the aldehyde stage for primary alcohols.

Therefore, treatment of allyl alcohol with $$MnO_2$$ gives acrolein (propenal) in a single step.

Why the other options do not work:
• $$H_2O_2$$ is too mild; it does not perform this selective oxidation.
• $$OsO_4$$ adds across the double bond to give a diol rather than oxidising the -CH$$_2$$OH group.
• $$KMnO_4$$ under oxidative conditions would cleave the C=C bond or over-oxidise the aldehyde to a carboxylic acid.

Hence, the correct reagent is Option A: MnO2.