Yes it's relatively easy to split water into Hydrogen and Oxygen, Christ it's a first year chemistry experiment with a satisfying 'Pop' to get the sprogs oohing and ahhing but you need to make it in much larger volumes, using energy and compress it to a liquid, using energy, in order to store it in a car in the amounts needed to feed the engine.
The claims of the Meyers engine specifically is that it's a 'perpetual motion' device whereby the energy used to creating the fuel is equal to the energy obtained from the fuel and there must also be zero loss to friction, gas escape, wasted heat etc. that, put simply is an impossibility as it breaks the laws of physics.
Another point is that, If you can get 'X' amount of energy out of combining two Hydrogen atoms and one Oxygen into H20 via combustion then it must have taken that much energy to split the two Hydrogen atoms from one Oxygen atom in the first place. The cheat with Solar, Wind, Water, Nuclear and Fossil fuels is that you don't have to create the energy as it's already there for the taking and you just have to try and minimise the losses during the use of those 'fuels'.
You simply don't get something for nothing and that is what we all, as a species, have to understand and what we need to do is figure out how best to work with what we do have and, when it comes to 'portable' energy then Fossil fuels are the only game in town. I fully believe that fossil fuels can be made 'clean' but it would need a willingness amongst car manufacturers, chemists, engineers and governments to really get to the best and cleanest way to do it but, and here is the big but that I believe the oil companies want to avoid, is that it would take a significant reduction in the cost of the fuels to make it financially viable to make good, clean burning vehicles and it's more profitable to sell the snake oil of electric cars.