Menahot, Chapter Three, Mishnah Three
1) Two minhahs from which the handfuls had not yet been taken out were mixed together:
a) If it is still possible to take the handful from each separately, they are valid;
b) If not, they are invalid.
2) If the handful [of a minhah] was mixed with a minhah from which the handful had not yet been taken, he must not burn it.
a) If he did burn it, then the minhah from which the handful had been taken fulfills the owner’s obligation while the other from which the handful had not been taken does not fulfill the owner’s obligation.
3) If the handful was mixed with the remainder of the minhah or with the remainder of another minhah, it must not be burned;
a) If he did burn it does fulfill the owner’s obligation.
4) If the handful had become unclean and yet he offered it, the head plate renders it acceptable,
5) But if it went out [of the Temple Court] and was afterwards he offered it, the headplate does not render it acceptable.
6) For the headplate renders acceptable only an offering which was unclean but not that which was taken out.
Section one: In order for the minhah to be validated, the handful must be removed. So if two minhahs are mixed in together and neither has their handful removed, each minhah will be permitted only if he can definitely remove a handful from each minhah, and he can tell that this handful comes from only one minhah. If it is impossible to tell which minhah is which, then neither is valid because he cant tell whether he has removed a handful from each.
Section two: Here a handful from one minhah is mixed in with another minhah from which the handful has not been removed. He should not burn this entire mixture because only the handful is supposed to be burned, not the remainder of the minhah offering. He also cannot remove two handfuls because in each handful there may be flour from the other minhah.
However, if he does burn the entire mixture the minhah which had the handful removed counts as fulfilling the obligation of its owners because its handful was properly burned. The other minhah does not fulfill the owners obligation because it was completely burned and only the handful should have been burned.