# Can a planet have a 6 Earth-month rotation around it's star at the same time it has a 12 Earth-hour day? #

Yes.  You'd need to *significantly* reduce Earth's orbital speed around the Sun, while simultaneously reducing it's angular momentum.

# How does this work #

Not too easily, since putting retro-rockets on rotating masses the size of Earth is **really difficult**.

# is it possible? #

I doubt whether even a Dyson-sphere civilization could do it.

# How does this affect the climate #

Being much closer to the Sun, with less time each day (1) exposed to the Sun and (2) cooling off would **naturally** have a **severe** impact on the planet.  Probably would boil off all the water.

No, it wouldn't be habitable.