I don't understand SUMPRODUCT formula result

You appear to be missing a comma and some parens.

=SUMPRODUCT(--(YEAR(JOET2!$B$3:$B$4999)=2016),--(JOET2!$A$3:$A$4999=8568),--(MONTH(JOET2!$E$3:$E$4999)=7))

alternatively:

=SUMPRODUCT((YEAR(JOET2!$B$3:$B$4999)=2016)*(JOET2!$A$3:$A$4999=8568)*(MONTH(JOET2!$E$3:$E$4999)=7))

Hi,
if you have Excel 2007 you don't need to use SUMPRODUCT anymore, it was needed only in older versions, now you can do it with SUMIF or SUMIFS function.
Simple example of SUMIF function is here.

Other problem can be format of your data. if it is text maybe you just need to put "" in your formula like this:
=SUMPRODUCT(--(YEAR(JOET2!$B$3:$B$4999)="2016"),--(JOET2!$A$3:$A$4999)="8568")--(MONTH(JOET2!$E$3:$E$4999)="07")

It depends on format you have.
I hope this can help you fix this, if not just upload your file or sample and we can fix it

working the quotes fixed it