countif based on a date range

I have 2 columns, one containing a piece of data and one containing dates. I want to count how many times the data is in the first column, based on a specific date range in the 2nd column. I have attached a sample SSF with a better explanation inside it.

Given your Quarters are Calendar based you could just use a Pivot Table.

Set Region as Row Field
Set DOI as Column Field -> Right Click on this Field -> Group -> Quarters & Year
Set Region as Data Field -> set to COUNT

This will generate your matrix for you efficiently.

If you still wanted a formula (I'd use a PT myself) - assuming data is all one year:

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If not one year - add a YEAR test.