This a very broad question, so you may benefit from breaking it down into some specific areas to focus on.
Since this assignment focuses on the broader American perception of these groups in contrast to the reality of their differences, it may make sense to think a little bit about your existing knowledge before researching them in depth. This will give you an honest, first-hand window into how your lived American experience shapes that perception.
If you choose, for example, Japan, China, and Thailand, think about what you already know about each of these cultures. Have you eaten their food? Listened to their music? Watched any of their movies? Do you know anything about the specific history of these countries? How about the experience of people immigrating to the United States from these countries—do you know anything about that?
How did you come to learn these things? Were you taught them in school? Did you passively learn them through proximity to people of Japanese, Chinese, and Thai descent? Where are the strengths in your knowledge, and where are the weak points? Why do you think that is?
As you research the countries you choose, focus on the differences between them. There's an important clue in the question that suggests the type of answer your teacher is expecting: "given the significant differences." Your assignment should specifically focus on how different these cultures are from each other.
Do you think your preexisting knowledge of these countries is supported by what you found, or are you surprised by what you learned? Do you think your perception is representative of other American majority perspectives? Why or why not?