WordPress uploads folder path. how it is decided?

When you uploaded an image within the Edit Page screen for a page with a date of 06/01/2013, the media uploader will use the date of the page to set the sub-directory within the uploads folder.

This is expected behavior because the media uploader passes the post_date to the wp_upload_dir() function. See http://codex.wordpress.org/Function_Reference/wp_upload_dir#Important_Note

If you were to upload the image using just the media uploader, but NOT within a page or post, the file would be moved into the appropriate folder for the current date.

Check the permissions on the uploads folder and the 06 sub-folder. The uploads folder and included sub-folders should be set to 755.