You can delete any story that you are the author of
If you are an Organisation Admin, you can delete any story within your organisation
You can delete a story from two places:
the Story’s page - Story page
a Timeline that the story appears on - View stories in the Newsfeed or a on a Timeline
Steps
Go to the story’s page or the timeline that the story is on. (Consider using the Timeline Filters to find the story)
Click the cog icon that appears in the top right corner of the story
The story menu appears
Select Delete