A CHINESE GIRL

It sounds like this sentance is presenting a reason for someone to be late to a class.

It means a student told their professor that the tire on their car had went flat,( lost its air pressure ) causing them to have to stop to fix it, and that is why they are late to class.

A CHINESE GIRL
Thank you very much!!!

You are welcome. :-)

A diagram of the sentence would look something like this:

Main Clause
THEY = subject
TOLD = verb
THE PROFESSOR = direct object (of the verb "told")

Subordinate Clause
THAT = relative pronoun
THEY = subject of subordinate clause
HAD GOT = verb of subordinate clause
A ... TIRE = direct object (of the verb "had got")
FLAT = adjective (modifying "tire")
ON THE WAY BACK = prepositional phrase