how do i delete private browsing from the the tool bar

OK, I'll bite.... what tool bar?

Since you mention 'private browsing', I assume that means you're using some kind of web browser... which one? All of them have slightly different options and methods for customization.

That said, a quick check of Safari, Chrome and Firefox (which are the most popular browsers on Mac OS X) shows that none of them offer a 'private browsing' option on their tool bar. Therefore, without more data it's hard to give any advice.

The only thing i can suggest is the age-old solution of holding the Command (Apple) key and dragging the icon off the toolbar - that's a pseudo-standard way of removing toolbar icons. It might or might not work for you.