Last time I played, doom was at 2 and it advanced by 4 after the omen moved counterclockwise because of a Mythos card.
The first two doom advances awakened Yog, the following two should follow the awakened side of the AO's sheet's rules.
Yog's sheet says "Each time a Gate would cause Doom to advance, place that Gate on this sheet instead."
Well, 4 red gates caused doom to advance in sequence. Which two should I place on the AO's sheet? Am I allowed to choose in this case?
Yog-Sothoth awakens and doom advances
Posted answer in other thread where you cross posted the question. (tl;dr: yes, you can pick).