I know this is Ranger Fourm, that being said. I put a raditor in a 93 Explorer and now have a leak (antifreeze) at the rear of the engine. I checked the heater core, it is not leaking there, it is driping off the left (drivers) side of the transmission, are there any hoses back there?

 

Which engine does it have? Also I would check around the head, could have blown a head gasket and has an external leak. Not really sure without knowing which motor it has, but I'm pretty sure there's no coolant lines or fittings on the back drivers side of the engine.

Also noticed I'm not to far from you, if you need any help I might be able to swing by and give a helping hand.

 

You probably have the 4.0l engine.
Lower intake manifold has coolant passages for circulating coolant from one head to the other, my ranger had a coolant leak, on the front, from that head to intake gasket.

Hard to see back there but I would check where the head and intake meet, both sides.

Also small pin holes in hoses can spray coolant onto areas that normally wouldn't be a place where coolant could leak from, so if the leak point doesn't make sense, check the hoses carefully.

Problem with small leaks are that they don't leak until engine warms up and gets 15psi of pressure in the cooling system.
A cooling system pressure tester(you can rent these cheap) can help find a leak, you can pump up the cooling system pressure to 20psi, on a COLD engine, then look and feel around for the leak.

 

Could be the head freeze plug on the rear of the head.
Can you get a mirror in there and see.

My first Ranger had that problem.

Had to sue Ford for warranty repairs on that one.

 

3 litter engine, is in the explorer

 

Probably not, most Explorers were 4.0L v6s.