My guess would be that the question is mistyped.
Assuming that the question is correct, potassium carbonate and magnesium chloride should be the answer here.
Every mole of potassium carbonate dissolved in water dissociates completely to produce
#"K"_ 2"CO"_ (3(aq)) -> 2"K"_ ((aq))^(+) + "CO"_ (3(aq))^(2-)#
The same can be said about magnesium chloride
#"MgCl"_ (2(aq)) -> "Mg"_ ((aq))^(2+) + 2"Cl"_ ((aq))^(-)#
Mind you, the question is only interested in the number of moles of dissolved particles produced per mole of dissolved solute, i.e. in the van't Hoff factor, not in what happens to those ions in solution.
So my guess would be that the question was mistyped. This doesn't happen very often, but it does happen. It could be that you could be dealing with sodium chloride,
In both cases, potassium carbonate would be the correct answer.
Potassium carbonate and Magnesium chloride
- In case of Methanol, it will not dissociate into water so, 1 mole of it will produce only 1 mol of dissolved particles in solution.
- In case of Ammonium chloride and Sodium iodide, they dissociate to give 2 ions per mol of solute.Each produces 2 mol of dissolved particles in solution.
- In case of Potassium carbonate and Magnesium chloride , they dissociate to give 3 ions per solute.Each will produce 3 mol of ions when dissociate in water.
THUS, ANSWER IS POTASSIUM CARBONATE AND MAGNESIUM CHLORIDE.