"She wanted to hear what Greek and Latin sounded like"

Ancient Greek was spoken during several periods of Greek history, from c.3rd Century BC to 6th Century AD.  It is still considered to be one of the most important languages from a cultural and historical perspective, due to its use during the Age of Pericles, or Athenian Golden Age, of 448 BC to 429 BC.  It was during this time that much of the wonderful literature, sculpture, theatre and political discourse the ancient Greeks are so admired for were produced.  From the early Renaissance period to the 20th Century it was very much part of the core curriculum in education, and is frequently still learned today by those with an interest in Classical literature and history.

Latin was the language spoken in Ancient Rome and throughout the Roman Empire.  Although now classified as a ‘dead language’, it is still the official language of the Holy See in Rome, and is also used in the formation of new words in modern languages, for example in science.  Its daughter languages include Italian, French, Spanish, Catalan, Portuguese and Romanian.  Very beautiful and precise in its Classical form, it is still widely taught, and even a rudimentary knowledge can assist greatly in the learning of the modern European languages listed above.  If you fancy learning a bit of Latin, here is a great introduction: