So I started reading new 52/rebirth Superman. In the Lois and Clark miniseries we see Superman save hank henshaw thinking he could prevent him from becoming cyborg Superman. Fast forward to the action comics revenge arc we all of a sudden see hank become cyborg Superman and mongul even remember who he was. How is this even possible if cyborg Superman never even existed yet? It’s confusing
I remember in new 52 green lantern we are told about how Mongul and cyborg Superman destroyed coast city yet Superman finds hank henshaw and says he’s trying to prevent hank from becoming cyborg Superman.
Then in action comics we see hank become cyborg Superman and all of a sudden Mongul knows who he is. This makes no sense to me.
I think you just found a moment of bad editorial continuity upkeep. During the New 52, it was never 100% clear how much of Post-Crisis continuity survived and what did. It sounds like the writers of New 52 Green Lantern assumed that the Reign of the Supermen story where Mongul and Cyborg Supes destroy Coast City was still continuity in New 52. It sounds like Dan Jurgens assumed that Reign of the Supermen and the creation of Cyborg Superman never happened in the New 52 world. Apparently, the editor of the Lois and Clark miniseries was unaware of the Green Lantern reference. That’s just my best guess, though. This kind of thing happened a lot during the New 52, so you may have just stumbled across a continuity error.
Anyway, in the end, I think Hank Henshaw used some kind of powerful artifact to regain his Cyborg Superman abilities (but it’s been a while since I read that story). Also, after the Post-Crisis Superman combined with the New 52 Superman, history changed to a combination of both Post-Crisis and New 52 (at least in Superman stories) and that would explain why Mongul recognizes Cyborg Supes.
Oh! While researching your question, I was reminded of something else. Not to confuse you more but, in the New 52, there was a different version of Cyborg Superman. That Cyborg Superman wasn’t Hank Henshaw. It was Zor-El, Supergirl’s father, under Braniac’s control. This Cyborg Supes probably wasn’t meant to be the one that helped destroy Coast City (at least I can’t remember any indication that he was), but you could probably headcannon retcon that it was him that teamed up with Mongul in the New 52 universe if that makes it easier…?