COUNTIFS to count data in two columns based on other criteria?

Hi

Im having problems with COUNTIFS and multiple criteria. I am trying to count the number of times a name appears in two columns D:E, this based on the date (Month / Year),
The formula is on the "Stats" sheet, along with the cells to select the Year etc.

Im struggling to describe well so i have attached a copy to show what i mean (unfortunately have had to sanitise it somewhat). There is a note in the relevant cell.

Hope you can help (you have never let me down before)!

Thanks in advance.

Si