"Vous avez des carottes."
Translation:You have carrots.
I used to know how to spell carrots in english before I started learning to spell carottes in french.
Both mean "you" but tu is used with friends and close acquaintances. Vous to address more than one person (plural) or to address a person that you don't know well (singular) or to whom you owe respect (singular).
When I hear 'vous' then 's' is silent but when it is 'vous avez' then 's 'is not silent. Could anyone please explain this to me ?
What you hear is a liaison. In order to get that smooth euphonic sound in French, words ending in a silent consonant but followed by a word beginning in a vowel (or h meut) may carry that consonant sound onto the vowel word.
vous avez → vou z-avez
elles ont → elle z-ont
mes enfants → me z-enfants
You can find more information here.
I've translated "des legumes" for "vegetables", without "the" and Duoling correct me. Now I translated "des carrottes" for "the carrot" and Duoling correct me too. Am I expect to use "the" meaning "des" or not?
Des carottes does not mean "the" carrots.
If it is translated at all you can put "some," though honestly nothing at all is usually best. It is the plural indefinite article. (un/une singular, des plural) This article doesn't exist in English. For example:
une carotte → a carrot
des carottes → carrots
This is not to be confused with the possessive (of + the) de + les → des : les jupes des filles → the girls' skirts.