We can add the asterisk before and after the certain partial string or substring, and then apply the COUNTIF function to count cells in Excel.

Select a blank cell you will place the counting result at, type the formula =COUNTIF(A1:A16,"*Anne*") (A1:A16 is the range you will count cells, and Anne is the certain partial string) into it, and press the Enter key.

And then it counts out the total number of cells containing the partial string. See screenshot:

Note: For counting cells containing both substrings, you can apply this formula =COUNTIFS(A1:A16,"*Anne*",A1:A16,"*Green*") (A1:A16 is the range you will count cells, both Anne and Green are the certain partial strings).

If you have Kutools for Excel installed, it will be much easier to count the number of cells containing partial strings or substrings in specified selection.

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1. Select the range where you will count cells if partial string/substring matched, and click Kutools > Select > Select Specific Cells. See left screenshot:

2. In the opening Select Specific Cells dialog box, please:
(1) Check the Cell option in the Selection type section;
(2) Select Contains from the first drop down list in the Specific type section, and then type the certain partial string or substring into right box;
(3) Click the Ok button.

And then a dialog box pops out and shows how many cells contain the certain substring or substring. See screenshot:

You can close this dialog box with clicking the OK button. Meanwhile, all matched cells are selected immediately in the specified selection.

Note: For counting the number of cells containing two partial strings or substrings, you can specify the settings in the Select Specific Cells dialog box as below screenshot shown: