To answer this question, we need to have knowledge about the Mughal emperors of India and their timeline.
Option A) Delhi Sultanate - This option is incorrect because the Delhi Sultanate refers to a Muslim kingdom in North India from the 13th to the 16th century, and it is not specific to any particular ruler.
Option B) Humayun - This option is incorrect. Although Humayun was a Mughal emperor of India, he ruled from 1530-1540 and 1555-1556. He is the father of the emperor mentioned in the question.
Option C) Abbas the Great - This option is incorrect. Abbas the Great was a Safavid Shah of Iran, not a Mughal emperor of India.
Option D) Akbar the Great - This option is correct. Akbar the Great was a Mughal emperor of India from 1556-1605. He took the throne at the age of 13 and was the grandson of Babar, the founder of the Mughal Empire in India.
The correct answer is D) Akbar the Great. This option is correct because Akbar fits the given description as the Mughal emperor who ruled from 1556-1605, took the throne at age 13, and was the grandson of Babar.