In this story, the conflict between the siblings is resolved through the intervention of God.
At the beginning of this chapter, Miriam and Aaron are jealous of Moses. They feel that they are important and that God has spoken through them as well as through Moses. For this reason (and because Moses had married a Cushite), they were upset. This conflict between them and Moses was arbitrated by God. God told Miriam and Aaron that Moses was special and that no one else had as much favor in God's eyes as him. God then punished Miriam (but not Aaron) for speaking out against Moses. This put an end to the problem between the siblings.