"She finished reading the letter."
Translation:Lei finì di leggere la lettera.
Any reason why "di" is necessary? "Lei finì leggere la lettera" was marked wrong.
Finire di leggere is an aspectual construction, the preposition between the two verbs is required.
Only modal verbs (and few others) can be followed directly by a second verb.
You can refer to these old discussions for details:
Without "di", it basically reads, "She finished to read the letter".
With "di" it is more along the lines of, "She finished of reading the letter."
Neither sounds quite correct in English, but the second one is a bit more relatable, I think.