This question is about translating the phrase in the title, which is problem 8 of Drill IV of Unit 1 in Hansen and Quinn’s Greek: An Intensive Course (on Attic Greek).
I understand the phrase literally reads “the soul (acc.) of Homer (gen.).” But page 29 of the text discusses three ways a noun modifier can be in “attributive position”: by being interposed between the article of the noun and the noun itself (την του ´Ομερου ψυχην); by appearing after the noun, but with a repetition of the noun’s article (την ψυχην την του ´Ομερου); or the same as the second case, but without the first instance of the noun’s article.
The phrase I am asking about has none of these forms, so — according to these rules — the genitive is not in attributive position. The text does say, “The genitive showing possession usually appears in the attributive position but may appear outside of it.”
I am left wondering, though, whether there is a notable stylistic difference when the genitive of possession is not in attributive position. Does it convey a different emphasis or tone that could be captured in English translation? Is it more colloquial, say, than the more formal attributive uses?