The correct answer is A) stop-check valves installed in the bilge suction manifolds. Stop-check valves installed in the bilge suction manifolds prevent accidental flooding of the engine room bilges through the bilge system. These valves allow water to be pumped out of the bilges but prevent backflow and unintentional flooding. The other options are not specifically designed to prevent this type of accidental flooding. For example, using a positive displacement reciprocating bilge pump (B) or installing eductors in the bilge rose boxes (C) do not directly address the issue of backflow prevention. Installing a swing check valve before each bilge valve (D) could also work, but stop-check valves are the more common and effective solution for this purpose.