"I am not afraid!"
Translation:Mie nu mi-e frică!
"mi-e frică" ("I am afraid") is the more grammatically correct form, similarly to "mi-e foame" (I'm hungry), "mi-e sete" (i'm thirsty), "mi-e dor (de ___)" (i miss (something/someone)). "Eu nu am frică" is not grammatically incorrect, but it is an antiquated form of the construction which aligns more with the English "I have no fear", and which in Romanian is also asking for a direct complement (what do I have no fear of?) e.g. "Eu nu am frică de întuneric." - "I have no fear of the dark." - this object needs to be a general and unspecifiable object (e.g. not "nu am frică de el" (i have no fear of him), but "nu am frică de înălțime" (i have no fear of heights). Note that "frică" is the only one that can accept such a construction (e.g. "nu am dor de mama" - "i have no longing for mother" or "nu am foame" (I have no hunger) is completely agrammatical).
TL:DR - not wrong, but the difference between the two is one of nuance only, so just stick to the "mi-e ____" constructions when you're learning as it's much more straightforward.