the period from January 1st 300 BC, 00:00 to December 31st 201 BC, 23:59
in 4th century B.C. it was the year 400 B.C. and ended in 301 B.C.
2300-2400 years ago
The correct answer is fourth century, in which fourth is spelled out and century has a lowercase c.
It is grammatically correct to spell out the word for numbers of ten and less, hence, "second century B.C." is correct.