We have given the hand to the Egyptians, and to the Assyrians, to be satisfied with bread. We have given the hand to - in token of submission (note, Jeremiah 50:15).
To the Egyptians - at the death of Josiah, when the King of Egypt deposed Josiah's son, Jehoahaz, from the throne, and put Eliakim or Jehoiakim in his stead (2 Chronicles 36:3-4).
And to the Assyrians - i:e., the Chaldeans, who occupied the empire which Assyria had held. So in Jeremiah 2:18 "Assyria" is used for Chaldea.
To be satisfied with bread - (Deuteronomy 28:48, "Therefore shalt thou serve thine enemies ... in hunger, and in thirst, and in nakedness, and in want of all things").