"I will get the check this time."
My Chinese teacher has taught that the use of 次 is flexible; 我这次买单 should be accepted.
A native Chinese clarified this for me. She said that the normal style is 这次我买单, but it is also acceptable to say it in the other order 我这次买单. Perhaps Duolingo will get around to adjusting this eventually.
"maidan" should be written as "埋单“. "买“ is a very common spelling error made by those who are ignorant of the word's Cantonese orgin.