Ha!  The scam persists -- some things never die!

Do this, and your battery will die -- it takes more energy to
electrolyse the water into hydrogen and oxygen that you get back by
burning the hydrogen.  So where does that extra energy have to come
from?  The battery, of course.

If this scheme worked, the world would be knee deep in perpetual
motion machines, and we never would have heard of OPEC.

Now, if you used electricity from the local utility to create the
hydrogen, instead of your car's battery, you would save on gas, but
you will still pay more than the cost of the gas in terms of higher
electricity bills.  YOU would be greener, but if your local electric
utility uses coal, then you would be actually hurting the environment,
and having a larger carbon footprint that you were before.