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I did say that 8 and 12 weren’t coprime.
That isn’t true. You can do EXACTLY what he did. If he had packs of 8 hot dogs and 9 buns, removing one bun from each pack would have the same effect. And 8 and 9 are coprime.
And you can also do what I said he could’ve done, that is, get an even number of hot dogs and buns by purchasing different amounts of packages. If someone purchased 9 packs of 8 hot dogs and 8 packs of 9 buns, they would even out.
You can ensure any two coprime integers go into another number evenly by simply making them factors of the other number (in this case, 72).
Edit: fixed a typo