A useful shortcut is to treat "eutectoid" and "peritectoid" as the solid-state versions of "eutectic" and "peritectic," simply replacing the liquid phase in each with a solid.
- Eutectic reaction: its solid-state analogue is the eutectoid, in which a single solid splits into two on cooling. Neither the eutectic nor eutectoid form matches a reaction that combines two solids into one.
- Peritectic reaction: here a liquid reacts with a solid to give a new solid. Turning the liquid into a solid gives its analogue, which is exactly two solids combining to give a third.
- Eutectoid reaction: as noted, this splits one solid into two, the reverse direction of combination described in the question.
- Peritectoid reaction: this is precisely the solid-only analogue of the peritectic reaction, two solids reacting together to produce a third solid on cooling, exactly the transformation given.
Replacing the liquid in a peritectic reaction with a solid gives exactly the peritectoid reaction described in the question.
Therefore, the correct answer is Peritectoid reaction.