Here "hand" represents power or control. Alternate translation: "I will allow the enemies who want to kill Pharaoh Hophra, the king of Egypt, to defeat him" (See: [[rc://en/ta/man/jit/figs-metonymy]])
Here "hand" represents power or control. And, Nebuchadnezzar represents his whole army. The phrase "sought his life" is an idiom that means to want to kill someone. Alternate translation: "when I allowed the army of Nebuchadnezzar to defeat Zedekiah king of Judah" (See: [[rc://en/ta/man/jit/figs-metonymy]] and [[rc://en/ta/man/jit/figs-idiom]])