I'm editing a file using SharePoint Designer. Where is the folder
url("/_layouts/images/) stored on the server?
Rob Windsor has said it above, but I wanted to give it "answer" status. While the _layouts folder does indeed live at:
c:\program files\common files\microsoft shared\web server extensions\12 (SharePoint 2007)
c:\program files\common files\microsoft shared\web server extensions\14 (SharePoint 2010)
\Program Files\Common Files\microsoft shared\Web Server Extensions\15 (SharePoint 2013)
SharePoint Designer will not allow you to open those pages.
The folder "_layouts/images" is a mapped folder in the web server. It maps to the server directory "c:\program files\common files\microsoft shared\web server extensions\14\layouts\images".
With SharePoint Designer you can only edit files stored in the Content Database, which are generally all files that are not in a directory starting with and underscore like "_layouts", "_vti_bin", etc.
If you need to modify Images, you have to upload them to a document library and change the former reference to the "_layouts/images/..." in the file referencing your image (page, master page, page layout, etc.). These files can usually be edited in SharePoint Designer.
look under 14 hive (if using sp2010) or 12 for sp 2007