Hi NB,
COUNTIFS is your friend here.
COUNTIF can handle only one comparison. In this case you want to count occurrences that fall within a one calendar year period.
Put into words, you want the occurrences on or after the first day of the year AND before the first day of the next year.
Here's an example, using your sample data:
Column B contains the Date & Time values that are to be counted.
Cell D2 contains the number 2019, which the first DATE will use to construct the 'smallest' date for which the dates will be counted, and the second DATE will calculate the date 12 months later.
D3 contains the number of the following year, used by the copy of the formula in row 3.
Translated to English, the formula in E2 says:
Count the rows in which the date is on or after the first day of the year in D2 AND is before the first day of the month 12 months later. As the formula is filled down,the row of the D2 reference will increment by one for each row.
Copy/paste version of the formula:
COUNTIFS(B,">="&DATE(D2,1,1),B,"<"&EDATE(DATE(D2,1,1),12))
Regards,
Barry