If there is a G-d, why did he allow six million Jews to die in the Holocaust?

This is a difficult question that has no easy answers. However, rather than think of the six million killed, think of the twelve million left alive. The Holocaust was an attempt to thwart the purposes of G-d with regard to the Jewish people. If Hitler had had his way, there would be no Jews left alive today. But G-d has preserved the Jewish people through almost four thousand years of history, as he promised (see Deuteronomy 4:31). G-d has been active in the lives of the Jewish people throughout their history, and even in our own generation G-d has demonstrated his love of the Jewish people by bringing them back to the land of Israel. G-d gave man the ability to choose love, peace and humility; but, unfortunately, man preferred hatred, war, and pride. G-d mourns over these poor choices but does not override our ability to decide.