You won't be able to, because your document is a giant image and Acrobat is not Photoshop.
If you just need a hardcopy without the headers, click File > Print and change the "Print What" setting to "Document and comments." This will cause your white boxes to take effect when you print. However, other Acrobat 6.x users will need to make the same settings change. Also, the covered information will still be present in the file. If you are redacting a sensitive document, this will NOT be sufficient to release to the public in PDF form.
If this is a 1-page PDF file, another solution would be to open the document straight into Photoshop and use the drawing tools to blot out or crop off the part you want removed.