Commentary for Numbers 19:12

הוא יתחטא בו HE SHALL PURIFY HIMSELF WITH IT — with this ash.

ואם לא יתחטא וגו', “if such a person does not undergo sprinkling of these waters and ashes on the third and seventh day, etc.” Nachmanides writes (in his commentary on verse 20) that the thrust of this verse is to inform us that purification is impossible without the above steps, although the person that had embarked on the purification process had already undergone immersion in a ritual bath. We know that this need for a ritual bath first is also a requirement from Leviticus 17,16 ואם לא יכבס....ונשאו עונו, “if he does not immerse himself in a ritual bath he will bear his guilt.”

With the ashes of the cow. Rashi is answering the question: Scripture should have stated "with it" in the feminine form, given that it refers to the cow. Therefore, he explains “with the ashes” meaning that [בו] refers to the אפר (ashes) which is a masculine noun.