What year did the shang dynasty overthrow the xia dynasty?

That's a very difficult question to answer because the Shang Dynasty was founded when the last Xia ruler was overthrown. So to find out when he was overthrown, one only need know when the Shang Dynasty was founded. Therein lies the problem: There is no exact date on the founding of the Shang dynasty. Only speculation. For instance, Lin Xin, Chinese historian, astronomer, and editor during the Xin Dynasty, says the Shang ruled between 1766 BC and 1122 BC, while the Bamboo Annals (a chronicle of ancient China) has the Shang Dynasty ruling between 1556 BC and 1046 BC, and the Xia Shang Zhou Chronology Project places them between 1600 BC and 1046 BC. To further complicate the issue, some consider the Xia Dynasty to be completely mythical.