Sorry, I know this is an old thread, but I don't get on the forum so much lately and I just saw it today for the first time.
There are a lot of preconceptions flying around here, mostly based on the idea that the 4-stroke engine as we know it is the pinnacle of design and that's the way it has to be. In fact, the design of engines is based on a variety of factors, not only on performance and efficiency. A lot of it has to do with basic economics, as well as simplicity of design, and what is considered "normal" practice.
Basic thermodynamics tells you that if you can burn yourself on the exhaust pipe, your engine is inefficient. The fact that you can throw a bucket of water on the muffler and create steam means that the engine is capable of greater power output, assuming that a system is designed to harvest the extra energy. Water injection has been used since the 1930s to create momentary extra power to allow overloaded aircraft to take off. It's done with regular 4-stroke engines as well as turbine engines, with little to no alteration to their normal function. Water injection in 4-stroke engines has also been used in race cars.
A frequently ignored fact about the typical internal combustion engine is that a large part of the cooling of an engine is accomplished by dumping extra fuel into the cylinder and not burning it. If you run an engine at the stoichiometric ratio of 14.7:1 (the ratio where there is exactly the correct amount of oxygen and fuel to completely combine) you will create a lot of power and a lot of heat. An engine can handle this level of heat if it is made of ceramics or fancy alloys, which are expensive. The customary solution to this problem is to use a richer fuel mixture and build the engine from iron and/or aluminum (and size the cylinder and ring to fit at a temperature suitable for these materials). The richer fuel mixture allows enough fuel to make power to move your car down the road, while the extra fuel absorbs the extra heat and dissipates it through thermal expansion. For those who are interested in air pollution, in the old days this unburned fuel used to fly out the exhaust pipe. Nowadays, the extra fuel is burned in the catalytic converter, where it is turned into a huge amount of extremely useless heat.
The concept of water injection addresses the problem of dissipating extra heat from the cylinder. The idea is to use only the fuel that is to be burned, and add water mist to take up the extra heat. The water turns to steam, with an expansion ratio of 1600:1, which is about ten times the expansion ratio of vaporizing unburned gasoline. This means that while burning the same amount of fuel and producing the same amount of heat, replacing the extra gasoline that's used for cooling with water will produce a lot more expansion, meaning that more power is extracted from the fuel that is burned.
This can be done, and has been done, in normal 4 stroke engines. I've never heard of a 6 stroke engine before, but it makes sense that all of that extra heat coming out the exhaust pipe could be harnessed if a mechanical system were designed to capture it.