The correct answer to this open question is the following.
You forgot to include the options for this question and the graphic that shows the statistic. However, we can say the following.
The theory that would be most valuable for explaining the percentage difference between Millennials versus young adults in the 1980s who were living in their parent(s)' homes would be the Looking-Glass Self theory.
The reason why is because this theory establishes that people base the way they feel about themselves regarding the opinions of other people. When these people interact with others in what commonly is known as social interaction is when they realize the opinions of other people.
The above-mentioned graphic shows a statistic of 25 to 35 years old that are living in the house of their parents.