If you already know the background knowledge, the Reddit comment’s key point is: There’s a 748-state Turing machine that (is isomorphic to a program that) grin

If you already know the background knowledge, the Reddit comment’s key point is: There’s a 748-state Turing machine that (is isomorphic to a program that) grinds out all the provable theorems of ZFC and halts if it proves contradictory theorems. Calculating BB(748) under ZFC requires proving that this program never halts, which would double as a proof of ZFC’s — and therefore its own — consistency. By Gödel’s Incompleteness, you can’t do that (as a system can’t prove it’s own consistency).