This is not a great chapter in the history of the people of Israel. Moses was up on the mountain getting the ten commandments which had been written by the finger of God when the people of Israel, led by Aaron, are up to no good. Notice the personal touch, literally, of the commandments handed down to Moses. Remember that Joshua is with Moses up on that mountain.
While they are up on the mountain they become restless and Aaron leads them into making a golden calf that they could worship. Below you will see a golden calf that was worshiped in Egypt, and so would have felt very familiar to the Israelites who had just left Egypt.
God tells Moses what the people are doing even while Moses is up on the mountain. He tells Moses that he is going to destroy the people of Israel and just raise up a branch from him. But Moses pleads to him to save the people, and actually God “changed his mind about the disaster that he planned to bring on his people”. This is not the only time that we see God “change his mind”. If you look at Jonah 3:10 you read: “God changed his mind about the calamity that he had said he would bring upon them; and he did not do it.”
Some feel threatened that God can actually change his mind. You have Hebrews 13:8 that tells us: “Jesus Christ is the same yesterday and today and forever.” This makes us think that God cannot change his mind. God can do anything that God wants. The implication of a mind change is that a mistake has been made or that somehow the Providence of God is limited. No, the change is always for our good. You never see God changing his mind from saving the people to destroying the people. Thank God for that! It is always God changes His mind from destruction to redemption. That is just a part of God’s nature, that He wants the best for us.