Your two moon signs form an angle 90 degrees apart creating a Square relation.
There may be many challenges in this relationship. A compromise is needed from one of you to overcome the ill feeling you may have on each other. You may share considerable understanding and opinion, along with respect for each other. Your Moon signs indicate that you are not very well matched.
Cancer is typically a Moon sign of emotions, instinct and intuition and a Libra Moon is one of charm, harmony and indecision. Together you each may find some success in this relationship, though only with a compromise from one of you.