You wrap the end of the cable around a ball and pull it into the hole. If you don't have the ball that came out of your old cable then a ball out of a wheel bearing will work.
https://www.motoalliance.com/Site.TechSupport.ViperATVUTVWinches.LineStopperInstallation.go
https://www.motoalliance.com/Site.TechSupport.ViperATVUTVWinches.LineStopperInstallation.go