Why not nosso instead of nossos. 'Our' is plural. adding the 's' is like overkill.
Portuguese possessive words equivalent to "my", "your", "our" and "their" are adjectives and like most Portuguese adjectives vary with the gender and number of the thing they describe.
I said jacket instead of coat and was marked wrong. Is there another word in Portuguese for jacket?
I don't think "casaco" is necessarily wrong depending on the style of jacket. Other words are "jaqueta", "paletó" (suit jacket) and "smoking" (a great word for a dinner jacket).
So if I wanted to say "the women's coats," should I say "os casacos das mulheres"?