We would also say a date as tenth March. I keep getting those marked as wrong.
You probably get marked wrong, Belinda347865, because you are following the British convention, as lambisqueiro's link explained. DL was set up in the U. S., and gives preference to New World spellings and conventions. This is not to say that other regions shouldn't contribute. They absolutely should.
Doesn't matter what English grammar rules say, Spanish has its own rules and we have to follow them whether we like them or not.
Why on earth would you want to impose English grammar rules on a different language? If you want to learn another language, you have to learn what is preferable to native speakers if you hope to communicate successfully.
If not, How would you say that in English?
Since it's in a form of question, and there is no question word to start the sentence, the correst answer would actually be "can't you travel on March 10"
"March twelfth" is acceptable English. I'd say your preference for "twelfth of March" is just that, a preference.
Except that "the tenth/twelfth of March" more closely follows the spanish grammer "el diez de Marzo". But thank you for reminding me how to spell "twelfth".