The two prayers in Exodus 32 are both by Moses and both are intercessory prayers on behalf of the people of Israel. The Israelites, though having just been brought out of Egypt after the plagues and God’s parting of the Red Sea, have already forgotten the care of the Lord and think that Moses has abandoned them. So they go to Aaron demanding that they be given gods to worship (perhaps this is the influence of all those years of being around Egyptian polytheism). For some reason, Aaron gives in to their demands and makes an idol in the form of a golden calf. God, of course, sees this going on and tells Moses what the people have done and says that he is going to destroy the nation because they have forgotten him and made an idol. But Moses intercedes for the people, not because any merit of their own, but he speaks to the covenant faithfulness of God. He speaks of God’s mighty deeds in Egypt (32:11) and how destroying the nation will destroy the Egyptians’ view of God and any respect they may have had for him if he brings them out of Egyptian bondage just to kill them in the wilderness (v.12). Moses also brings up God’s covenant with Abraham, Isaac, and Jacob. Though wiping out the people and starting from scratch through Moses would still be in line with the covenant, forgiving the sin and continuing with this people would be a testament to God’s mercy and longsuffering. God hears Moses and relents from the destruction.