Chinese Near Year starts on a（d ）day

Each Chinese month matches a lunar orbit starting at a new moon, and so the start of the year is on the first new moon of the year.
Chinese New Year (CNY) or Spring Festival (chun jie ) can fall on a day ranging between January 20th to February 21st, however the extreme dates are rather rare, the next year that CNY falls on February 21st is 2319. This is just like Easter falling very late or very early. Another name for CNY is nong li xin nian (literally 'lunar calendar' new year), you may also note that the name includes the 'nong' character representing 'agriculture' so this tells you something about its origins in the 'sui' year.
One of the simplest ways to approximately calculate the date of Chinese New Year is to tie it in with the sui calendar and put it on the day of the new moon closest to (before or after) the first jieqi - lichun the beginning of the sui year. Alternatively CNY usually falls on the second new moon from the Winter Solstice (December 22nd). Neither of these is 100% reliable when CNY is very early or very late as there are small corrections to be made which only astronomers and mathematicians will appreciate.