why does my explorer sport 4wd shift hard with a clunk

What's your transmission fluid condition and level?

You haven't said if yours is manual or automatic. ..............................Or if you're in 4WD when this happens. IF AUTO its most likely that OR it could just be accumulated wear to the rear driveshaft's u-joints, gear slop in the rear and/or front end differentials, the transfer case, and/or the front driveshaft 's u joints or CV's. all being a little worn and the clearances stacking up to make for a LOT of play in the system. All other things being equal an automatic trans will usually add even more play to the system than a manual trans. If you've got more than about 75k on them, my first suspect would be the rear drive shaft's u-joints. To check for play in the REAR part of the drive train, put it in gear or park, put it in 2WD, jack up the rear end, put a chalk mark on one rear tire, grab onto the driveshaft to keep it from moving and rotate one rear wheel all the way forward until the slack is gone, then rotate it back until its gone. Measure the difference from chalk mark forward to to chalk mark back .More than say 2" would most likely be noticible as a definite clunk imn an auto trans shifting into Drive or Reverse. Unless your tires are vastly oversized from spec. You can check the total slack from the tranny FORWARD similarly through the transfer case out to the front wheels-(with it in 4WD of course). Is either forward or reverse worse than the other or D worse than D2?

The transfer case? Some clunking can be normal.