Mishnayos Parah Perek 4 Mishnah 3

שרפה שלא בעצים – that he kindled the fire with the body of the cow/heifer.

כשרה – that “wood” is not written in the Torah, but [only] "ושרף"/”and he shall burn [the cow in his sight]” (Numbers 19:5) plainly/merely.

או בכל עצים – that he didn’t burn it (i.e., the cow) with cedar wood, pine and cypress and wood of fig trees that are taught [in the Mishnah] in the chapter above (see Tractate Parah, Chapter 3, Mishnah 8).

הפשיטה ונתחה כשרה (if he stripped/flayed it and dissected it) – it is written (Numbers 19:5): “[The cow shall be burned in its sight -] its hide, flesh [and blood shall be burned],” whether through flaying and dissecting it or whether attached.

על מנת לאכול מבשרה או לשתות מדמה כשרה – and specifically to eat and to drink that the first Tanna/teacher validates it, that with all of the sacrifices also in that manner it is kosher/fit, as it is taught in the Mishnah in the [Third] Chapter “All the Invalid”/כל הפסולים (Mishnah 3, [folio 35a], he thought about eating something that he generally doesn’t eat, it is kosher/fit, as for example, from the food of the Altar for a person, but if he thought on the condition to sprinkle from its blood on the morrow, the first Tanna/teacher invalidates, for the All-Merciful calls it a “sin-offering.” But Rabbi Eliezer holds that thought does not invalidate with regard to a cow at all, even with sprinklings. But he goes according to his reasoning that what is done not for its own sake he validates at the beginning of our chapter (see Chapter 4, Mishnah 1), which has no law from the laws of Holy Things, since it was performed outside [the Temple walls]. But the Halakha is not according to Rabbi Eliezer.