‘which reaction would most likely require the use of an inert electrode?

An inert electrode is made up of non reactive metals like Platinum

An inert is electrode is required in one of the half cells or both the cells if there is no solid conducting metal in either half reaction. Or we can say that if in any half reaction neither product nor reactant is in solid phase.

From the given equations it is clear that

a) in first cell we have Cu and Ag in solid phase in either side

b) In second reaction the iron is in aqueous phase on both the side of reactant and product

so for reduction of iron or in cathodic half cell we need inert electrode [which does not participate in reaction]

Hence answer is

c) in third reaction Zn and Sn are in solid phase in either side

d) in fourth reaction Al and Ni are in solid phase in either side