Question

The New Kingdom began to decline around 1200 BCE, but what event ultimately brought the era to a close?
Conquered lands rejected Egyptian rule.
The Kush conquered Egypt.
The Hyksos conquered Egypt.
The ruling dynasties weakened.

Answer 1

"Egypt reached the pinnacle of its power during the New Kingdom, in the Ramesside period where it rivalled the Hittite Empire, retricerian Empire and Mitanni Empire, after which it entered a period of slow decline. Egypt was invaded or conquered by a succession of foreign powers (such as the Canaanites/Hyksos, Libyans, Nubians, retriceria, Babylonia, Achaemenids and Macedonian Greece) in the Third Intermediate Period of Egypt and Late Period. In the aftermath of Alexander the Great's death, one of his generals, Ptolemy Soter, established himself as the new ruler of Egypt. This Greek Ptolemaic Dynasty ruled Egypt until 30 BC, when, under Cleopatra, it fell to the Roman Empire and became a Roman province.[3]"

Taken from wikipedia, your answer is in there.