"He wants to sell the new sandals."
Translation:Calceos novos vendere vult.
A number of sources do not agree with this picture. See:
Please note that Vindolanda is a Roman archeological site in the UK. Excavation is ongoing there. There are other words for "sandal". Calcei served the role of a dress shoe (worn with a toga); Martial says they were hot in the summertime.
I disagree that you can omit the subject in the first sentence, since unlike with the first and second person, the gender is not fully known until after it's been stated. In later sentences, or if it can be inferred from other elements, it's fine. But otherwise you have to state it for a faithful translation.
We need a plural form for "new," since the "shoes" / "sandals" that are being described as "new" are themselves plural.
"He wants to sell the new shoes/sandals." WHAT he wants to sell, the direct object of the verb, will be accusative case; and, in this sentence, plural and masculine: calceōs novōs .
In another sentence, perhaps "The new shoes are in the country house," the new shoes are the subject of the verb, thus nominative, plural masculine: Calceī novī sunt in vīllā .
For the adjective to describe the noun, they must share the same C, N, G ( = case, number, gender).