Hi Vanessa,

To say, 'I like carrots', you have to use the definite article,  les and say -

J'aime les carottes 

It sort of indicates in French that you like all the carrots in the world. very strange!

Des is a partitive article meaning 'some' so you might say -

Je voudrais des carottes,  s'il vous plait = I'd like some carrots, please

or 

Donnez-moi des carottes = Give me some carrots

Hope this helps!