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.