Each option represents a specific number of dynasties that were established in the early eighth century AD.

Option 1 suggests that only one of the dynasties was established during this period. Option 2 suggests that two of these dynasties were established in the early eighth century AD. Option 3 suggests that three of these dynasties were established during this era.

Option 4, which is the correct answer, indicates that none of these dynasties were established in the early eighth century AD.

To break it down further, the Hoysala dynasty was established in the late 10th century AD, the Gahadavala dynasty in the mid-11th century AD, the Kakatiya dynasty around the end of the 12th century AD and the Yadava dynasty in the late 12th century AD. None of these coincide with the early eighth century AD, hence option 4 (`None`) is correct.