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The water is coming from your fuel tank. There is no place on the engine where water and fuel mix. Some larger engines have water cooled fuel, but not yours. Remove the fuel line going to the engine. Get a glass jar and using the primer bulb fill the jar about 1/2 way with fuel. Let it sit for a little bit and check to see if the water separates from the fuel.
If any water, drain the fuel tank, clean it out and put fresh fuel in. Is it a portable tank?
If a vent was open and the tank exposed and you had rain it could get in that way. But I would guess it was already in the tank from condensation or maybe some bad fuel. It was just mixed in previously.
Drain the carbs as well into some paper towels, then once you have filled the tank with fresh fuel and the carb drains still open squeeze the primer bulb to clean all the bad fuel out of the engine, then close the float bowl drains and start the engine. Make sure you clean up any spilled fuel.
post back ny questions and what tank you have.
If pumping the primer bulb helps keep the engine running then look for either an air leak at a fitting or a weak, failing fuel pump. I would be leaning towards a weak fuel pump not keeping the carbs full.