The governing principle in a marine heat-exchanger system is a closed engine-coolant loop that sheds its heat to raw sea water in the exchanger cores, driven round by the engine coolant pump.

The expansion tank sits at the high point to allow for coolant expansion and to keep the loop full; the flow we trace begins as coolant leaves this tank.

From there the coolant passes around the cooling cores of the heat exchanger, where the surrounding raw water carries its heat overboard.

The now-cooled coolant next flows through the oil cooler, picking up and removing heat from the lubricating oil.

It then returns to the engine coolant pump inlet, which pushes it back through the engine to complete the closed circuit.

The option sending coolant direct to the engine first ignores that it must be cooled in the cores before re-entering the engine, so it reverses the useful order.

Routing it to the exhaust manifold first, or through a keel coil back to the expansion tank, does not match the standard core-then-oil-cooler-then-pump path of this system.

Hence, the answer is Around cores, to oil cooler, to engine coolant pump inlet.