On my Facebook wall there are posts when some of my friends become friends with someone else.How to hide them?

Not really. Your friends can change the setting not to show you when they do this activity, but you can't filter it out. You can make it so your profile doesn't post this information, but you can't ignore the posts from other people. Privacy settings are difficult to change on facebook, but you can keep your profile from updating others on who you've become friends with, etc. There is a pretty simple way to filter out particular application notices however. When a post comes up from an application you don't use, such as FarmVille, hover on the right hand side and an edit tab will appear. Options to ignore every post from that friend or to ignore every post from that application will appear. If you click to ignore all application posts, no FarmVille posts will appear on your page from any of your friends. This can help a lot. There is also some sort of 'facebook light' or limited profile option where you don't get all these inadvertent posts, but I'm not sure what all it actually filters out.