Interviewers are more interested you show that you know the regulations of the operation that you are operating under. If you are coming from the CFI world then don't worry about the 6-6-6 rule. You can say that you've been reading about, you're not quite sure, but it goes something like... if you've been operating 91 all this time then don't sweat it. If you have been operating with the exemption then you better know it like the back of your hand.
As far as Domestic/Flag/Supplemental...When a company applies to be a part 121 carrier they have to declare if they are going to be a Domestic/Flag/or Supplemental carrier. These are different "types" of airlines as recognized by the FAA and they are all required to follow different "sections" of 121 (even though the regs are mixed together). From a pilot perspective, probably the two main differences are the Fuel requirements and the crew duty time and flight time limitation requirements. Generally Domestic is the most restrictive, Flag (International) is next, followed by Supplemental (i.e. charter operators).
Like most posts about 121 point out here, it is not very useful to study Part 121 regulations by themselves. What really needs to happen at your operation is spelled out in the ops specs and the operations manuals. There can be a mixing of all 3 in a single airline.
For example, American Eagle Airlines is a Domestic Airline that flies to International destinations. When they fly to International destinations they are still bound by domestic rules even though it is technically a "flag" operation. American Eagle Executive (SJU & MIA, a seperate 121 certificate) follow flag rules in all of their operations even though many of their flights are "domestic" flights. American Airlines has their pilots divided into two divisions, International and Domestic, before flying International pilots must have Flag required rest while Domestic pilots must have domestic rest even though an International pilot may do a domestic leg or vice versa, they must still comply with the regulations of their section. Island Air in Hawaii follows Domestic rules for all purposes except crew rest, where an exemption in the rules allows them to follow flag rules for crew rest purposes only.
Anyway, the point is, forget trying to figure out all the examples above. Don't worry about 121 regs until you get to a 121 airline. When you get to Indoc, take your ops specs, operations manual, and a copy of Part 121 and see how they are all interlinked for that particular airlines operation. It will only make sense once you have all 3 documents in front of you.
No interviewer is going to expect you to know every nuiance of the 121 regs. Just don't BS, if you don't know, you don't know.
Good luck.
Later