The Mizbeach (altar) had a red line that separated the top from the bottom half. The blood of korbanot (offerings) generally—the olah (burnt offering), the asham (guilt offering), the shelamim (peace offerings), the bechor (firstborn offering), the Ma'aser (tithe), and the Pesach (Passover offering)—is applied below the line. The blood of the korban chatat (sin offering) is applied above the line. Here we'll talk about what happens if blood of the chatat is mixed with blood of a different type of korban.
The Mishnah says that if blood that is supposed to be applied below the line—the blood of most korbanot—was mixed with blood that should be applied above the line, the blood of the korban chatat, Reb Eliezer says that you apply the blood above the red line, as with the korban chatat. The Kohen (priest) applies it above the red line. I view the blood of the korban that's supposed to be applied below the red line as if it were water. Right now, I'm applying above the red line. Therefore, I view everything else as water at this moment in time. I view it as nonconsequential, and I'm really only having Kavanah (in mind) to apply the korban chatat. Then I go back and apply the mixture below the red line. I also have in mind that I'm doing this for whatever is supposed to be below the line, and I'm fulfilling the zerikah (application) requirements for the other korban. Basically, it's a mindset change, according to the opinion here of Reb Eliezer. At first, you start off one way, and then you go the other way.
The Chachamim (Sages) say that the water should be poured into the pipe that goes into the courtyard of the Beit HaMikdash. There's no permitted way to apply it onto the Mizbeach. No matter what, you have a mix. You can't regard some of it as water in the beginning and then later change your mind. You have to have in mind that it's going in one spot. Here you have a mix, and you can't apply it to one spot if it's not supposed to be there. Therefore, he recommends that there's no permitted way to apply it to the Mizbeach, so you pour it down that pipe. But if the Kohen did not ask the Rabbi what to do, but went ahead and applied the mixture above the red line, then the application is valid for a korban chatat.