This is how to do it:
1. Log into your Facebook Page.
2. Click on the word "Activity" on top of the page.
3. Then scroll down and click on Activity Log link.
4. Now you can see the whole list of activities (like, comment or post) which you have done.
5. Look for that particular item which you like to delete.
6. On the right side of that item there is a pencil icon.
7. Click on it and a drop menu appear.
8. There are four options for you to click on: Highlighted on Page, Allowed on Page, Hidden from Page and Delete.
9. If you want to delete, then click on the word "Delete".
10. A box pops up that asks:Are you sure you want to delete this?
11. Click on the blue color Delete Post button.
12. Immediately it is gone.
That's how you delete shared post on your Facebook Page.