These cables worked perfectly for my 7 ft garage door even though the loops were larger than what I replaced. You don't need to tape the loops or anything - just make sure your garage door has the right amount of tension. There's plenty of info about this on the web, but basically you either use vise grips to slightly turn the bar and loop back over the wheel, or to loosen the screws and adjust the wheel itself. I replaced the jacked up cable in the attached image with this part. This is a copy/paste from a Q&A I answered earlier. Just trying to help.
Purchased these cables as replacements for my garage door cables that broke. Installation was easy due to the large hoops for the door, but it came as a catch 22 as they would often come off the hook. The solution? Wrapped some masking tape around the rest of the hoop so that it wouldn't come off! Haven't had too many issues since.