Question

Earth's rotational axis completes one precession every _____.

Answer 1

A). Earth completes one rotation on its rotation axis
every (3 minutes and 56 seconds less than 24 hours).
This causes night and day.  It's rotation, not precession.

B).  Earth completes one orbital revolution around the sun
every (365 plus a little bit) days.  It's revolution, not precession.

C).  I'm not sure what happens on a cycle of 512 years.
It may have something to do with the moon.  But whatever
it is, it's not precession.

D).  When you spin a top and it starts to run down, the first
thing that happens is that the handle of the top, or the point
on top of the top, starts moving in a circle.  That's precession.
That's what the Earth's axis is doing.  The north pole points
toward the north star (Polaris) now.  But the north pole is
actually drawing out a big circle in the sky, and other stars
will become the "north star" far in the future.
The north pole draws out a full circle in the sky, roughly
once every 26,000 years.  That's precession.