"Passengers connecting from an ANA international flight to an ANA domestic flight can proceed with through check-in at the international departure airport. It may be necessary to check in your baggage again due to customs.
Please note that through check-in service may not be offered at some airports.

*Through baggage check-in can be accepted only when it is a same day connection."

** Same day as what, they're not clear. If they mean, the same day as the international flight departs, that is impossible as of course one crosses the date line coming from the US. Or are they talking about a check-in for a domestic flight that leaves the same day as the international flight *arrives*, not the same day as the international flight *departs*? (That would seem to make sense, they obviously don't want to store bags for domestic flights that would leave the next day or even later than the day after the international flight arrived.) But I've learned to be wary and double-check absolutely every assumption....