The first time we meet Han Solo, he’s being confronted by a bounty hunter named Greedo. The alien says he owes money, but why didn’t Han Solo pay Jabba?
Han Solo didn’t pay Jabba because an Imperial Cruiser scared him into dropping a shipment. It’s implied that Han was a smuggler for Jabba, and the cost of the lost shipment was something he didn’t pay back.
Greedo warns Han that Jabba put a price on his head. Every bounty hunter in the galaxy will be looking for him.
Han Solo explains why he didn’t pay Jabba
In Star Wars: Episode IV – A New Hope, Luke and Obi-Wan enter the Mos Eisley Cantina. Princess Leia asks Obi-Wan for help transporting vital Rebel plans to her father on Alderaan, and the Cantina could provide a pilot capable of commandeering the trip.
Obi-Wan speaks with a Wookie, Chewbacca, as Luke heads to the bar by himself. In only a few moments, Luke is harassed by two aliens. The aliens brag that they’re wanted men with death sentences on 12 systems.
Noticing the thugs won’t leave Luke alone, Obi-Wan intervenes. Angered, one of the aliens pushes Luke to the ground and quick-draws their blaster. In self-defense, Obi-Wan uses his lightsaber in the Cantina and cuts off the alien’s arm.
Once the action calms down, Obi-Wan informs Luke that Chewbacca is first mate on a ship that may be suitable for the journey to Alderaan.
The ship captain says to the group that he’s Han Solo, pilot of the Millennium Falcon. He informs Obi-Wan and Luke that his ship is indeed fast, making the Kessel Run in less than 12 parsecs.
After the group irons out the financial mandatories of the trip, Obi-Wan and Luke hide from Imperial Troopers canvassing the Cantina. Once the coast is clear, Han stands up to join the group.
Han is confronted by Greedo
He’s stopped by a blaster aimed at his chest. Greedo, a bounty hunter, confronts Han about money he owes Jabba The Hutt. He says it’s too late for excuses and Han should have paid Jabba when he had the chance.
Greedo says that Jabba has put a price on Han’s head so large that every bounty hunter in the galaxy will be looking for him. The alien bounty hunter says he’s lucky he finds Han first.
Han insists he has the money he owes Jabba. Greedo offers Han the chance to him give the money he owes Jabba. In exchange, he will be let go. Not having the money with him, Han tells Greedo to speak with Jabba but is interrupted.
Greedo says Jabba is through with Han. He says Jabba has no time for smugglers who drop their shipments at the first sign of an Imperial cruiser.
Han admits even he gets boarded sometimes, and he didn’t have a choice but to drop the shipment into space.
So that’s the answer. Han Solo didn’t pay Jabba because an Imperial Cruiser scared him into dropping his shipment.