[i]Normally[/i], just pulling out the Ghost displays the Challenges on the right side of the screen,.just like in any PvE activity. However, there is a current issue Bungie is investigating that somehow makes Crucible Challenges in Quickplay not appear. That's probably what you are experiencing.
The issue is noted here: https://www.bungie.net/en/Forum/Post/239718019/0/0
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Thank you so much. I won’t go crazy now.
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Happy to help!