State the number of days needed for the moon to show a complete cycle of phases from one full moon to
the next full moon when viewed from new york state.

After reviewing the data table you listed above, the number of days that are needed for the moon to show a complete cycle of phases in New York State from one full moon to the next is 29 to 30 days. Either number can be used because of the number of days in a month will change. It will be either 29 or 30, no more or no less. 

Earths place in space