Sometimes you think better of an item shared on Facebook, whether it's a link you posted or a photo of you that someone else has shared. While you can't delete another person's tagged posts that include you, you can remove tags and hide posts from your personal Timeline. You can delete your own posts or change visibility settings so that items cannot be shared with people you do not know.
Unsharing an Item You Shared
You can easily remove an item if you shared it by accident, or have changed your mind about sharing it. When you press the "Like" button, the button changes so that you can click the "x" on it to unlike the item. This removes it from your Timeline. If you've shared an item, you can remove it from your profile directly. Go to your profile and click the down arrow that appears in the upper right corner. of the item, then click "Delete."
Removing a Shared Item From Another User
Your posts aren't the only ones people can view on your Timeline; if someone tags you in a shared post, it shows up on your page. To remove these posts from your Timeline, you can either remove the tag or hide it from your Timeline. The procedure for this is the same as if you were deleting your own post. First, hover over it to reveal the down arrow in the upper right corner. Click the arrow, then select either "Remove Tag" or "Hide from Timeline."
Changing the Privacy of Posts
Facebook uses the audience selector tool to control posts that you want to keep visible to a limited group of friends. Next to every one of your posts on Facebook you'll see a little icon of people; if you select this, you'll see your post's visibility options. Posts can be fully public or completely private. You can also set it so only friends can see your post, or make a customized filter that only allows some friends to see your posts.
Using the Activity Log to Hide or Delete Posts
If you're unsure of what you have shared and how visible it is, visit your Activity Log. The button for it is available at the top of your profile, in the lower right corner of your cover photo. This allows you to see all of your activity on Facebook. From the left sidebar you can filter that down to posts you have shared, posts others have shared or tagged on your Timeline, and even specific types of posts. The pencil icon on the far right of each item allows you to either change the privacy of a post, or remove it from your Timeline.