In the given electrochemical cell, the reduction half-reaction occurs at the electrode on the right side of the double vertical line (||).
To determine the reduction half-reaction, we need to compare the standard reduction potentials (E°) of the species involved. The half-reaction with the more positive E° value will be the reduction half-reaction.
Looking up the standard reduction potentials in a reference table, we find that the standard reduction potential for the Mn2+/Mn couple is -1.18 V, and the standard reduction potential for the Fe3+/Fe2+ couple is +0.77 V.
Since the Fe3+/Fe2+ couple has a more positive standard reduction potential, it will undergo reduction. Therefore, the reduction half-reaction is:
Fe3+(aq) + e- → Fe2+(aq)
I hope this helps!