When you post on someone's Facebook profile, both you and that person have the option to hide your post. This deletes it from view. Unless you remember exactly when you posted the content, it can be difficult to tell if it's been hidden. By comparing the posts you've written to what actually shows on the person's page, you can see if the content was hidden and whether the person is hiding all of your posts.
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Visit the page of the Facebook friend in question. In the top right, click "See friendship" to show your recent content together.
Scroll through the wall posts in the middle of the screen. If all the posts are from the other person and yours are missing, he or she has been hiding your posts.
Post something on his or her wall and make note of the two or three previous posts so you know where it should be. Check back in a day or two to see if it's still there.