As we learned on yesterday’s daf (=page) there were different activities that were done to the menahot as part of the ceremonial Temple service. Specifically, the two activities were hagashah – bringing the offering to the altar prior to performing kemitzah on the flour – and tenufah – lifting or “waving” the offering.
The “east” and “west” mentioned refer to the eastern side of the altar – where the entrance from the ezrat yisrael to the ezrat kohanim was located – and the western side of the altar which was referred to as bein ha-ulam la-mizbe’ah, between the sanctuary and the altar, which had a higher level of holiness.
Rashi explains that there is no obligation to perform tenufah on the eastern side of the altar, the Mishnah is teaching that even the eastern side is considered lifnei Ha-Shem – before God – as required by the Torah (see Vayikra 6:7), and tenufahon that side would be sufficient. The western side of the altar would certainly be appropriate for tenufah, as well.
The Rambam appears to disagree and require that tenufah be performed specifically on the eastern side of the altar. The Gri”z – Rav Yitzhak Soloveitchik – explains that this requirement stems from the fact that all who enter the Temple enter from the eastern side, so they first pass the eastern side of the altar, which is their first opportunity to perform the mitzvah. Given the general principle that ein ma’avirin al ha-mitzvot – that one should not pass on the opportunity to perform a mitzvah – tenufah should be done immediately at that point, followed by hagashah at the south-west corner of the altar, as required.