"You start classes on September second."
Translation:Tú empiezas las clases el dos de septiembre.
It is wrong...
The only "ordinal number" (first, second, third, etc.) used in Spanish dates is "Primero".
All other dates use "cardinal numbers" (two, three, four, etc.).
You're trying to literally translate it rather than translating it in the way the Spanish write their dates:
Formula for Saying the Date in Spanish
el + day + de + month (+ de + year)
So, September second=
el dos de septiembre.
Yes, apart from changing your word order for the date*, I think the idea is Duolingo wants you to show that you know the Spanish words for numbers, so wants you to write dos rather than 2. After all, if you are speaking rather than writing you need to say dos. So I think their approach is right.
* What is acceptable word order in English does not necessarily apply to Spanish.