Translation:Why do Turkish girls like Italian men a lot?
That doesn't seem entirely right to me. How about
erkek : man/male
erkek-ler : making it plural
erkek-ler-i : marking the noun compound
erkek-ler-i-n-i : adding the accusative marker, with -n- as buffer
I am not positive about the order of compound marker vs. the accusative marker. So any needed corrections are welcome!
I think it's close, but no cigar. If the Italian men were the subject, "they" would have to be "spelled" without the extra "ni"; its job is to show that "İtalyan erkeklerini" is a direct object.
Oh yeah, I also wanted to say that "like Italian men a lot" sounds a little strange. I think "like Italian men so much" sounds "much" more natural.