Question: Which king of Babylon installed Zedekiah as king of Judah after he defeated Pharaoh Necho at the Battle of Carchemish?

Context paragraphs:
Khedebneithirbinet I: Khedebneithirbinet I (“Neith Kills the Evil Eye”) was an ancient Egyptian queen from the 26th Dynasty, probably the wife of pharaoh Necho II and the mother of his successor, Psamtik II.

Necho II: Necho II (sometimes Nekau, Neku, Nechoh, or Nikuu; Greek: Νεχώς Β' or Νεχώ Β') of Egypt was a king of the 26th Dynasty (610–595 BC).  Necho undertook a number of construction projects across his kingdom.  In his reign, according to the Greek historian Herodotus (4.42), Necho II sent out an expedition of Phoenicians, which in three years sailed from the Red Sea around Africa to the mouth of the Nile.  His son, Psammetichus II, upon succession may have removed Necho's name from monuments.

Siege of Jerusalem (597 BC): In 605 BC, Nebuchadnezzar II, king of Babylon defeated Pharaoh Necho at the Battle of Carchemish, and subsequently invaded Judah.  To avoid the destruction of Jerusalem, King Jehoiakim of Judah, in his third year, changed allegiances from Egypt to Babylon.  He paid tribute from the treasury in Jerusalem, some temple artifacts and some of the royal family and nobility as hostages.  In 601 BC, during the fourth year of his reign, Nebuchadnezzar unsuccessfully attempted to invade Egypt and was repulsed with heavy losses.  The failure led to numerous rebellions among the states of the Levant which owed allegiance to Babylon, including Judah, where King Jehoiakim stopped paying tribute to Nebuchadnezzar and took a pro-Egyptian position.

Ishmael son of Nethaniah: Ishmael (Hebrew: ישמעאל "God shall hear") ben (= 'son of') Nethaniah was a member of the royal household of Judah who, according to biblical accounts in II Kings and Jeremiah, assassinated Gedaliah after he was appointed governor of Judah by king Nebuchadnezzar of Babylon.  The biblical accounts suggest (and have perhaps been edited specifically for this purpose) that Ishmael ben Nethaniah’s actions were a key factor in the subsequent flight of the people of Judah to Egypt, something Jeremiah counsels strongly against (Jeremiah 42 - 43).  Nonetheless, the people, led by Johanan son of Kareah, ignore his advice and depart for Egypt (Jeremiah 43:6).

Zedekiah: Zedekiah ( ; ; Greek: Σεδεκίας, "Sedekías"; Latin: "Sedecias" ), also written Tzidkiyahu, was a biblical character, the last king of Judah before the destruction of the kingdom by Babylon.  Zedekiah had been installed as king of Judah by Nebuchadnezzar II, king of Babylon, after a siege of Jerusalem in 597 BC, to succeed his nephew, Jeconiah, who was overthrown as king after a reign of only three months and ten days.

Battle of Zephath: The Battle of Zephath, according to the Bible, occurred during the dates of 911-870 BCE, in the reign of King Asa of Judah.  It was fought at the Valley of Zephath near Maresha in what is now Israel, between the armies of the Kingdom of Judah under the command of King Asa and that of the Kushites and ancient Egyptians under the command of Zerah the Ethiopian who, given the time frame with Asa's reign, may either be Pharaoh Osorkon II or Osorkon I.  The warriors of Judah were victorious in the battle after utterly defeating the Egyptians and Kushites, by divine intervention as written in the Bible and Asa's forces collected a large volume of war spoils.  Asa's forces pursued the enemy stragglers as far as the coastal city of Gerar, where they halted due to exhaustion.  The result of the battle created peace between Judah and Egypt until the time of Josiah some centuries later, when the latter would again make encroachments in the region.

Mulek: According to the Book of Mormon, Mulek ( ) was the only surviving son of Zedekiah, the last King of Judah, after the Babylonian conquest of Jerusalem.  The Book of Mormon states that after escaping from Judah, Mulek traveled to the Americas and established a civilization there.  Although the word Mulekites does not appear in the record, these people of Mulek are today commonly referred to simply as "Mulekites".

Battle of Megiddo (609 BC): This Battle of Megiddo is recorded as having taken place in 609 BC when Pharaoh Necho II of Egypt lead his army to Carchemish (northern Syria) to join with his allies, the fading Neo-Assyrian Empire, against the surging Neo-Babylonian Empire.  This required passing through territory controlled by the Kingdom of Judah.  The Judaean king Josiah refused to let the Egyptians pass.  The Judaean forces battled the Egyptians at Megiddo, resulting in Josiah's death and his kingdom becoming a vassal state of Egypt.  The battle is recorded in the Bible, the Greek 1 Esdras, and the writings of Josephus.

Babylonian captivity: The Babylonian captivity or Babylonian exile is the period in Jewish history during which a number of people from the ancient Kingdom of Judah were captives in Babylonia.  After the Battle of Carchemish in 605 BCE, Nebuchadnezzar, the king of Babylon, besieged Jerusalem, resulting in tribute being paid by King Jehoiakim.  Jehoiakim refused to pay tribute in Nebuchadnezzar's fourth year, which led to another siege in Nebuchadnezzar's seventh year, culminating with the death of Jehoiakim and the exile of King Jeconiah, his court and many others; Jeconiah's successor Zedekiah and others were exiled in Nebuchadnezzar's eighteenth year; a later deportation occurred in Nebuchadnezzar's twenty-third year.  The dates, numbers of deportations, and numbers of deportees given in the biblical accounts vary.  These deportations are dated to 597 BCE for the first, with others dated at 587/586 BCE, and 582/581 BCE respectively.

Kuzi-Teshub: Kuzi-Teshub (also read as Kunzi-Teshub) was a Neo-Hittite King of Carchemish, reigning in the early to mid-12th century BC., likely in 1180 - 1150 BC.  He was the son of Talmi-Teshub, who was both the last viceroy of the Hittite Empire at Carchemish under Suppiluliuma II and a direct descendant of Suppiluliuma I.  Kuzi-Teshub reigned in Carchemish as well as in the later Neo-Hittite Melid/Malatya.

Supporting paragraphs: Zedekiah Siege of Jerusalem (597 BC)
Answer: Nebuchadnezzar II