"The child has a new cap."
Translation:L'enfant a une nouvelle casquette.
Some adjectives come before the nouns. You can remember this from "BANGS" - Beauty, Age, Number, Good/Bad, Size. Nouvelle falls inton the age category
"New" has two translations: one objective and one subjective.
L'enfant a une casquette neuve: objective, after the noun, the cap is brand new.
L'enfant a une nouvelle casquette: subjective, before the noun, the cap is new to him, and it may have been worn before, by the child or someone else.