Shevuos, Chapter 2, Mishnah 1. This Mishnah expands on what was stated in the first Mishnah of Chapter 1, and describes exactly what takes place in a case of unclear awareness. The Mishnah opens: "Yedi'ah setumah shtayim shehein arba" - unclear awareness, two that are four. In the first Mishnah we learned that the cases involving forgetting that one is tamei, forgetting about the Beis HaMikdash, or forgetting about the sacrificial food are two that are four - two that are really four, and now the Mishnah comes and spells them out.
The first case - tumah and eating sacrificial food:
"Nitma veyada, vene'elam mimenu hatumah vezachur es hakodesh" - a person became tamei and knows that he is tamei, and afterwards his tumah slipped his mind, but he remembers that the item he is about to eat is sacrificial food.
"Ne'elam mimenu hakodesh vezachur es hatumah" - he forgets that this is sacrificial meat and thinks it is ordinary meat, but he remembers that he is tamei.
The Mishnah adds: "Ne'elam mimenu zeh vazeh" - meaning that he forgot about both of them. This is not counted among the two that the Mishnah is coming to enumerate, but it is certainly included in them.
"Ve'ochel es hakodesh velo yada, umishe'achal yada - harei zeh be'oleh veyored" - and he eats the sacrificial food without knowing, and once he has eaten he becomes aware, this is a case of an oleh veyored offering. He does not remember that he is tamei, or he does not realize that this is sacrificial food, and he eats the sacrificial food without knowing; and after eating he again remembers that he was tamei and that this was sacrificial food. Since there is awareness at the beginning and awareness at the end, with only a lapse in between, he brings an oleh veyored offering, as we mentioned earlier.
The second case - tumah and entering the Mikdash:
"Nitma veyada, vene'elam mimenu hatumah vezachur es haMikdash" - he is tamei and knows it, and afterwards he forgets his tumah, but he remembers that this area is part of the Beis HaMikdash.
"Ne'elam mimenu haMikdash vezachur es hatumah" - he forgets that this is part of the Beis HaMikdash, but he remembers that he is tamei.
And likewise "Ne'elam mimenu zeh vazeh" - if he forgot both of them, this too is included.
"Venichnas laMikdash velo yada, umisheyatza yada - harei zeh be'oleh veyored" - and he entered the Mikdash without knowing, and once he left he became aware, this is a case of an oleh veyored offering. He entered the Mikdash without knowing that he was tamei, or without knowing that this was the Mikdash, and after leaving he remembered that he was tamei or that this was the Beis HaMikdash. Here too he brings an oleh veyored offering, since there is awareness at the beginning and awareness at the end, and in between a lapse - forgetting about the Beis HaMikdash, forgetting about the sacrificial food, or forgetting about the tumah.
In summary: In this Mishnah, the Mishnah explained the "two that are four" that were taught in Chapter 1: two cases of eating sacrificial food while tamei (his tumah slipped his mind while he remembered the sacrificial food, or the sacrificial food slipped his mind while he remembered the tumah), and two cases of entering the Mikdash while tamei (his tumah slipped his mind while he remembered the Mikdash, or the Mikdash slipped his mind while he remembered the tumah), as well as the case where both slipped his mind. In all of these, when there is awareness at the beginning and awareness at the end with a lapse in between, this is a case of an oleh veyored offering.