We have been given that Luna mixes 3/4 cup of orange juice with 3/8 cup of cranberry juice.
First of all, let us find the total amount of juice Luna had by adding the amount of orange juice to amount of cranberry juice.
Let us have a common denominator.
Since Luna gave 5/8 cup of juice to Mags, so let us subtract amount of juice given to Mags from the total amount of juice to find the amount of juice left in Luna's glass.
Therefore, the amount of juice left in Luna's glass is .