You can apply formulas to count the number of occurrences per year or per month in Excel. Please do as follows:

Select a blank cell you will place the counting result at, and type the formula =SUMPRODUCT((MONTH($A$2:$A$24)=F2)*(YEAR($A$2:$A$24)=$E$2)) into it, and then drag this cell’s AutoFill handle down to the range as you need. See screenshot:

Notes:
(1) In above formula, A2:A24 is the date column you will count per year/month, E2 is the specified year, F2 is the specified month, and you can change them as you need.
(2) For counting per month with ignoring year, you can apply this formula =SUMPRODUCT(1*(MONTH($A$2:$A$24)=F2)).

Easily select and count any date cells if dates are between two dates in Excel

If you have Kutools for Excel installed, you can apply its Select Special Cells utility to quickly select and count any date cells if dates are in a certain date range.

Actually, we can also create a PivotTable to count the number of occurrences per year, month, quarter, hours, seconds, etc. Please do as follows:

1. Select the table you will work with, and click Insert > PivotTable. See screenshot:

2. In the opening Create PivotTable dialog box, please specify the destination range you will place the PivotTable at, and click the OK button.

In our case, we check the Existing worksheet option, select the Cell E1 in active worksheet, and click the OK button. See screenshot:

2. Now the PivotTable Fields pane comes out. Please drag the Date column to the Rows section, and drag the Amount column to the Values sections.

And then the PivotTable is created as below screenshot shown:

3. Right click the values column title (Sum of Amount in our case), and select Summarize Values By > Count from the right-clicking menu.

4. Right click any cell in the Row Labels column, and select Group from the right-clicking menu.

5. Now in the opening Grouping dialog box, please select one or more grouping criteria from the By box, and click the OK button. See above screenshot.

In our case, we select both Months and Years in the By box. And you can select the proper criteria based on your needs.

And now it has counted the number of occurrences per year and month in the PivotTable. See below screenshot:

Note: When we group the row labels by month and year, a Years label will be added above the Date label in the Rows section in the PivotTable Fields pane. For counting the number of occurrences per month, you can move the Years label below the Date label. See below screenshot:
 

If you have Kutools for Excel installed, you can apply its utilities to count the number of occurrences per year/month/weekday/day, or year and month, or month and day, etc.

1. Select the date column, and click Kutools > Format > Apply Date Formatting. See screenshot:

2. In the opening Apply Date Formatting dialog box, please select the specified date formatting from the left Date formatting box, and click the Ok button. See above screenshot:

According to counting criteria, please select the specified date formatting, such as month, year, weekday, day, month and day, etc. In our case, we select one of the Month formatting, such as Mar.

3. Keep selecting the date column, and click Kutools > To Actual to convert dates to the month names.

4. Select the range you will count, and click Kutools > Content > Advanced Combine Rows. See screenshot:

5. In the opening Advanced Combine Rows dialog box, please do as follows (See above screenshot):
(1) Select the Date column, and click the Primary Key;
(2) Select the Amount column, and click Calculate > Count;
(3) Select other columns and specify the combination rules or calculation rules. In our case, we select the Fruit column, and click Combine > Comma.
(4) Click the Ok button.

And now it counts the number of occurrences per month. See below screenshot:

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