When in doubt, retell a character’s ‘origin story’.
Supergirl starts having what she believes are dreams where her parents are still alive. She believes that they may be in the Phantom Zone but surprisingly enough when she asks the criminals held there they keep their mouths shut. She then consults Comet the Super-Horse who uses his ESP powers to try to contact her parents. Comet is successful and receives a message that they are stuck in “the Zone” which Supergirl takes to mean the Phantom Zone.
Supergirl visits the Phantom Zone but the criminals are (obviously) not too helpful when she asks about her parents. She meets the criminal Jer-Em who seems to know something about Kara’s parent’s predicament but the other criminals psychically gang-up on him to shut him up. Supergirl then uses one of her most-useful deus ex machina: the Chronoscope. The Chronoscope lets the user view past events much like they were watching a movie.
Supergirl observes that after Argo City was saved from the destruction of Krypton but before it became inhospitable it flew (yup, it had jet engines) near a yellow sun. The citizens all gained super-powers which everyone loved except for Jer-Em! Jer-Em sabotaged the engines so that Argo City flew away from the yellow sun and was unable to fly back towards it thereby dooming all the city’s inhabitants. Jer-Em was sentenced to the Phantom Zone where he still resides.
Supergirl then observes her father’s first attempt at saving the citizens of Argo City. He found a dimension much like the Phantom Zone, but on a separate wavelength, which he called the Survival Zone. He created a Survival Zone projector but it seemed to not work. That’s when Zor-El decided to save his daughter by constructing a rocket ship. After the Kryptonite radiation had killed the rest of the Argo City citizens Zor-El and Allura started phasing into the Survival Zone! The Kryptonite radiation acted as a catalyst which fixed his device. Now that Supergirl knows her parents are safe but trapped in the Survival Zone she must find a way to help them!
On my patented Supergirl Wink © scale this issue gets: