Copyright © University of Cambridge. All rights reserved.
'Roll On' printed from https://nrich.maths.org/
$3$ times
In returning to its original position, the disc rolls a distance $3\pi d$. As the disc does not slip, it rolls out a distance of $\pi d$ when the disc makes one complete turn about its centre, so $3$ complete turns are made.
If you liked this problem,
here is an NRICH task which challenges you to use similar mathematical ideas.