I would say neutral engine off is the best way to travel. Idle in neutral would be second. Slowing down in gear would be next followed by pressing the brake following hitting the gas and brake at the same time.
When you are in gear and off the throttle you are engine breakin.and that's bad. Just don't use the brakes you will slow down the car when you do that. Only do it if you need to slow down.
I think there is like 1000 other threads with the same title. The entire community can't agree but if you are listening to information from a tv show I think you should do some more research. If I'm not mistaken many new cars are throwing out engine braking or dfco in favor of neutral. Audi comes to mind.
I also would like to add my girlfriend has gotten +3mpg in her automatic 2.5l v5 jetta coasting in neutral vs in gear. She is slowly picking up the hypermilling game one technique at a time.
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