Why can't my horse put his left hind leg down he can't move?

If your horse can't take any weight on the affected leg, you need to call the vet immediately. It is possible that he has dislocated a joint or broken the leg. Because a horse is so heavy and its legs so fragile, when a horse is unable to take weight on one of its legs the opposite leg (ie right hind, in this case) often buckles under the strain, so 'let's wait and see if it's any better in the morning' is the worst thing you can do in this case. The sooner you call the vet, the better your chance of saving the horse. A dislocation or damaged tendon can probably be repaired; a fracture probably can't, depending on its location. At any rate, he is probably in a lot of pain so please, please call the vet.