"Not at all" - it's the way to answer when somebody sasys "Спасибо" (Thank you). Another variant is "Пожалуйста" (You are wellcome). "Не за что" literally means that "there is no for what", it's just a polite form. 

don't mention it

[ne za shto]

Может быть имелось ввиду "ни за что" в смысле "нет"?

Спасибо Yuliia a Mary

[ne zʌ ʃtɔ]