The question is about where the initiator must dissolve for emulsion polymerization to work as intended. The key is to track the physical path a radical has to travel: it must be generated somewhere and then find its way into a monomer-swollen micelle to start a chain.
The defining feature of emulsion polymerization is that radical generation happens in the water phase and radicals then migrate into micelles, which only works if the initiator itself is water soluble.
Therefore, the correct answer is Soluble in water.