A few approaches in truth.
or if you know F2:F64 will always and only contain numbers (dates) [not the case here] then
or if you will not always be looking for a given year but variable dates (eg Jan-Jun) then:
SUMPRODUCT is not overly efficient so you could also consider using 2 SUMIFs (or SUMIFS XL2007+)
Finally... and not least... you might want to consider using a Pivot Table if the analysis is based on years etc (you can group the Date Field by Year) but again this would require only numbers in column F (not presently the case)
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