# the house of Judah will walk with the house of Israel

Here "walk with" represents being united. Alternate translation: "the people of Judah will be united with the people of Israel" (See: [[rc://en/ta/man/translate/figs-metaphor]])

# the house of Judah

The word "house" is a metonym for the family that lives in the house. In this case it refers to the kingdom of Judah, which included the descendants of Judah and Benjamin. Alternate translation: "Judah" or "the kingdom of Judah" or "the people of Judah" (See: [[rc://en/ta/man/translate/figs-metonymy]])

# the house of Israel

The word "house" is a metonym for the family that lives in the house. In this case it refers to the kingdom of Israel. Alternate translation: "Israel" or "the kingdom of Israel" or "the people of Israel" (See: [[rc://en/ta/man/translate/figs-metonymy]])

# the land that I gave your ancestors as an inheritance

God speaks of giving them the land to possess forever as if it were an inheritance. Alternate translation: "the land that I gave to your ancestors so that it would belong to their descendants forever" (See: [[rc://en/ta/man/translate/figs-metaphor]])