Ben Bennett,
Welcome to the forum!
The problem is that each criteria_range must be the same size. Because E2 is only 1 cell where the other ranges A2:B2 and C2:D2 are each 2 cells, the Countifs function returns an error.
So using a slight tweak, this should work for you:
As a side note, the formula you posted shows a return of "I" for a False output, but in your description you state that it should return an "F" for a False output. This has me a bit confused, but I went with the "I" as shown in the formula.
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