The Shulchan Aruch · Orach Chayim
אורח חיים קפ״הOrach Chayim 185
Siman 185 of 697 in Orach Chayim — 5 se'ifim
הלכות סעודהLaws of the Meal· siman 185
Se’if 1א׳
בִּרְכַּת הַמָּזוֹן נֶאֶמְרָה בְּכָל לָשׁוֹן.
Birkas Hamazon can be recited in any language
Se’if 2ב׳
צָרִיךְ שֶׁיַּשְׁמִיעַ לְאָזְנָיו מַה שֶּׁמּוֹצִיא בִּשְׂפָתָיו; וְאִם לֹא הִשְׁמִיעַ לְאָזְנָיו יָצָא, וּבִלְבַד שֶׁיּוֹצִיא בִּשְׂפָתָיו.
One needs to hear what he is reciting but if he does not hear he has fulfilled his obligation as long as he articulated the words
Se’if 3ג׳
יֵשׁ מִי שֶׁאוֹמֵר דְּבַעַל הַבַּיִת עִם בָּנָיו וְאִשְׁתּוֹ, צָרִיךְ לְבָרֵךְ בְּקוֹל רָם, כְּדֵי שֶׁיֵּצְאוּ בְּבִרְכָּתוֹ.
There is an opinion that that when a ba’al habayis is with his children and wife he must recite birkas hamazon out loud so they can discharge their obligation with his recitation
Shulchan Aruch, Orach Chayim — Torat Emet 363 edition, via Sefaria — public domain
English: Sefaria Community Translation — CC0