How do I politely move my neighbours hard board that they left infront of my front door?

Move it back to theirs.

Put it in front of their door and tell them you only accept soft boards in front of yours.

You dont have to politely anything if they put something in front of your door...that's so rude

The most polite way would be to ask them to come and get their door.

I’ve been reading through your question and the replies to it so that I don’t duplicate others’ advice, and man I have to say - this has more twists and turns than the US election! 😄

Since you can’t simply move it back to their side due to its weight, I would say call your complex manager and tell them you’d like it removed! I’m sure they have a maintenance staff with a couple of muscular people on it. 💪🏻

what exactly is a hard board? (besides a board that is hard)

Hide it.

Why do you keep saying “hard”.

If you have a fireplace; burn it. If it oak or other good hard wood then it is very expensive stuff so I would put in front of their door as they migh have had plans for it but they shouldn't leave in front of your door.

chuck it up on the roof