Parah, Chapter 4, Mishnah 2. This chapter lists the flaws that render the preparation of the parah adumah invalid. Our mishnah deals with two of them: the place where the cow was burned, and the manner in which its blood was sprinkled.
The mishnah's opening ruling concerns the site of the burning. "Serafah chutz migisah": she was burned somewhere other than her own pit. "O bishtei gitos": or her body was consumed in two separate pits. "O shesaraf shtayim": or he burned two cows, "begas achas", together within one pit. In every one of these cases the verdict is "psulah", the parah does not count.
The word "gas" refers to a hollowed out basin dug out in advance for this purpose, its shape recalling a winepress. Burn the cow anywhere but there, and she is disqualified. She is ruled out just the same when her body was divided, part of it consumed in one such basin and the remainder in a second. The mirror image fails as well: two cows, each brought out on its own, burned together inside a single basin. Every cow requires a burning place of its own and a turn of its own.
The next clause moves to the blood. "Hizah velo kiven": he did perform the sprinkling, but he did not aim it, "keneged hapesach", toward the opening, and therefore "psulah". The kohen had to be facing the doorway of the Beis Hamikdash at the moment the blood left his finger; blood thrown without that orientation leaves the cow unfit.
The mishnah now turns to the counting of the sprinklings. "Hizah mishishis shevi'is, chazar vehizah shevi'is, psulah": a seventh sprinkling taken from the blood of the sixth, followed by a further seventh, leaves the cow disqualified. "Mishevi'is sheminis, vechazar vehizah sheminis, kesheirah": an eighth taken from the blood of the seventh, followed by yet another eighth, and the cow remains fit.
To follow this we need the rule already established, that the kohen must dip his finger in the blood afresh for every single sprinkling. Now to the first case. He dipped for the sixth time and sprinkled his sixth sprinkling, and then, without dipping again, performed a seventh sprinkling with the blood left over on his finger from the sixth. That seventh sprinkling is worthless. And even if he now dips again and performs another seventh sprinkling, the parah remains unfit, because an invalid sprinkling has come between the six good ones and the new one, and the later sprinkling cannot join together with the earlier valid sprinklings across that break.
The second case is different. Here he dipped for the seventh time, sprinkled his seventh, and then with the leftover blood on his finger performed an eighth sprinkling, and afterward dipped again and performed yet another eighth sprinkling. The parah is fit, because the seven required sprinklings had already been completed properly before anything went wrong. Whatever extra and invalid sprinklings were added after that do not undo the seven that were done as they should have been.