This Mishnah talks about how the Kohanim (priests) would walk up the ramp to reach the upper half of the Mizbeach (altar) and do what they needed to do. There is a difference between the three Avodot (service) that we mentioned and other types of Avodah that were done in that upper part of the Mizbeach. We are not only talking about the Avodot that were done all the way at the top of the Mizbeach, like lighting the fire and flipping the Imurim, the parts of the offerings that they would burn. We are also talking about Avodot done by the Kohanim standing on the ledge. There was a ledge that went around the Mizbeach. They would stand there and apply the blood of the Chatat (sin offering) to the different corners of the Mizbeach. So we are talking about that as well. First we will talk about the other Avodot, and then we will talk about the three Avodot that we discussed in the last Mishnah.
The Mishnah says that all who went up the Mizbeach went up on the right side of the ramp. When they reached the end, they turned right and went all around the Mizbeach counterclockwise until they reached the place where they needed to do their Avodah. Once they were done, they continued around the Mizbeach in that same counterclockwise direction until they reached the other side of the ramp, and then they went down the left side of the ramp. So when they went up, they always went in the same direction, but they paused at the spot on the Mizbeach where they wanted to do their Avodah.
Even for the Avodot done on the ledge of the Mizbeach, which the Kohen had to walk up to, they would start there. They would start on the normal ramp and then veer off onto the side ramp that went to the ledge of the Mizbeach. They never went directly onto that side ramp. They always started on the normal ramp up to the Mizbeach, and then they might veer off. If you see a picture of this, there is a ledge where they can go from the regular ramp. They would never go backwards. They would never retrace their steps on the Mizbeach. They always went counterclockwise, fulfilling the ruling that you should continuously turn right at all of your turns, as the Gemara in Sukkah tells us. Continue to always go right. So at every turn they would go right, right, right until they reached the end. They would never pause for any reason other than the Avodah, and, as we said, they would never retrace their steps. Then they would go down on the left side of the ramp.
Now we will talk about what the Kohanim did for the three Avodot that we mentioned at the start of this Mishnah and in the last Mishnah. The rule that we mentioned in the last Mishnah applied to all of the Avodot except for the following three things. For these three different Avodot, they would go up the left side of the ramp. They would turn left when they reached the top of the ramp, and then walk directly a few steps to the southwest corner, where the Avodah was done. The Chozerin (those returning) would return the way they came when they were done with that Avodah. They went directly back down that ramp. They went down the left side of the ramp. So, if you can picture it, the Avodah was done right at the corner: they went up the left side, veered left, and did the Avodah in that corner, which is the southwest corner of the Mizbeach. Then they went right back down in the same direction they had come up the ramp. They went down the left side of the ramp. That is the Mishnah. That is what they did.
In these situations, the Kohen did not first turn right and circle the Mizbeach until he reached the southwest corner. That would be considered a very long route, and we are nervous that, during the Avodah of the wine and the water, they would absorb the smell of the fire of the Mizbeach, which would be a disgrace. It would disqualify the wine. And with the bird Olah (burnt offering), which was the third Avodah that we mentioned, we are nervous that the bird is going to breathe in all that smoke and die before the Avodah could be done. To avoid all these problems, we have the Kohen go directly to that spot, up the left side of the Mizbeach. After he is done with the Avodah, he would retrace his steps and go down that same side.

