The transnationalist approach discussed in the passage is in essence the concept of an Africa that transcends borders and incorporates the cultures and experiences of many countries. Let's keep that in mind as we go through the answers. We're looking for a potential historical study that exemplifies that thinking.
A talks about US versus European nationalist mythologies. While we discuss the nationalist mythology of the US in the passage, this study wouldn't exemplify the transnationlist ideology of 19th century African American historians, as it doesn't focus on transnational identities.
B suggests a study that focuses on US and European treatment of minorities, which may be an interesting study, but doesn't focus on transnational identities, but rather on subsets of certain nations.
C talks about the imperialism mentioned in the passage, which also doesn't focus on the transnationalism we're looking for.
D is getting a little closer by mentioning the emigrationist sentiments at the time, which could have some relation to the idea of a transnationalist African identity, but the study again doesn't focus on that.
E suggests a study that looks at how African American culture at the turn of the century incorporated several countries' cultures. This is transnationalist. Bridging multiple countries to incorporate each of them into one, larger, cohesive identity is fits what we're looking for. E is the correct answer.