The gemara (Brachos 20b) questions whether women are obligated in birkas hamazon min hatorah or only m’derabbanan. The Rishonim offer a number of reasons to explain why there should not be a Biblical obligation – women did not receive a portion in Eretz Yisrael which we give thanks for in bentching; women are not obligated to learn Torah which is mentioned in bentching; women do not have a bris milah, which we also thank Hashem for in bentching. The nafka minah whether the obligation is Biblical of Rabbinic is whether a woman could be motzi a man in bentching (side question: we might have expected a nafka minah to also be whether a woman who has a safeik whether or not she bentched has to repeat birkas hamazon, but this nafka minah is interestingly not offered by the gemara.) The Hagahos Ashri”i in Megillah rules that women are obligated in bentching min hatorah, but cannot be motzi men. Isn't this psak self-contrdictory – according to the gemara, if women are obligated in birkas hamzon min hatorah, they can be motzi men!? R’ Akiva Eiger explains that the gemara’s safeik was whether the exclusion from reciting the lines referring to bris, torah, or the Land of Israel exempt women from all of bentching, but there is no question that they cannot recite these particular lines. If a woman wishes to be motzi a man, he can listen to her bentching and fulfill his obligation through shome’a k’oneh, but would be forced to recite those few phrases himself. It was with respect to these particular phrases that the Hagahos Ashr’i wrote that a woman cannot be motzi a man.
R’ Akiva Eiger’s answer assumes that it is possible to mix shome’a k’oneh with dibbur in a single bracha. Returning to the question of whether shome’a k’oneh is to be taken literally as implying listening is speech or whether it is a seperate mechanism to fulfill mitzvvos, it seems to me that R’ Akiva Eiger is easier to understand if we take shome’a k’oneh as a form of speech, and therefore it can be combined with real dibbur. If it is a separate mechanism, how can a single bracha be fulfilled using two different means?