the rear end needs to be replaced
rear differential replacement on 2002 Ford Explorer
The labor to replace the rear end assembly is about 4 hours. Price of the parts depends on wether you have your rear end repaired or get a rebuilt unit. To get the correct rear end you need to supply the VIN number to the person you may be getting parts from and if your truck is 2WD or 4WD.
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Yours and about every other Explorer out there is bad. My suggestion would be is to go to a shop that specilzes in rebuilding rearends in place of having Ford do it. I have seen customers have much better luck doing it that way. P.S. Don't waste your money on a used one from a salvage yard. As you can see from the other responses what kinda qauility Ford has on their rearends The rest of the trucks are GREAT!