The term 'conflict' generally denotes a struggle between two or more things in any literary body of work. There are two types of conflict, 'internal conflict', which exists within the character's own being, and 'external conflict', which arises between the character and an outside force.
In the story "Catch the Moon", the main character Luis experiences both internal and external conflict. Since experiencing the death of his mum at a young age, he had been back and forth in juvenile hall. The conflict that arises out of such a tragedy is vast beyond measure. Since this, his relationship with his father began to deteriorate. This also worked to remove another parental figure from his life, thus intensifying his inner turmoil.
Subsequent to this, he formed a gang entitled "The Sharks." This created an even greater degree of separation between himself and his dad, due to his rebellious nature. Finally, he falls in love with a beautiful girl, Naomi. He tends to jump at her every whim. Through this, we can see that some of the internal and external conflicts in the story include,
Internal - Luis's grief over the loss of his mother and deteriorating relationship with his father
Luis's inability to control his impulses for Naomi, and deal with his feelings towards her in general
External - Luis conflict with his father over the gang, and his physical behaviour and impulses with Naomi.
I hope this answers your question.