"I like carrot very much."
Translation:मुझे गाजर बहुत पसंद है।
The Hindi sentence literally translates to something like 'To me, carrots are liked' which is why we use मुझे. This is the most common way of saying it. However, you can also rephrase it to 'मैं गाजर को बहुत पसंद करता हूँ।' where मैं is in the direct case.
There is no Hindi verb that is analogous to the English 'to like' so a 1-1 translation is not possible.