The correct answer is: C) 8th century CE
The rock-cut temples at Vizhinjam are believed to date back to the 8th century CE. This is based on the style of architecture, which is similar to other temples from that period. The temples are located on the coast of Kerala, India, and are a popular tourist destination.
Option A: The 4th century CE is too early. The earliest known rock-cut temples in India are from the 6th century CE.
Option B: The 6th century CE is possible, but the style of architecture is more similar to temples from the 8th century CE.
Option D: The 10th century CE is too late. The temples were abandoned in the 13th century CE, so they must have been built before then.
In conclusion, the rock-cut temples at Vizhinjam are believed to date back to the 8th century CE.