You can't parse the month and year from the dates in column A with sumifs or similar functions, you need to define a start and end date for the period and sum the values between those dates.
Assuming that your dates are in M/D/Y format, I think that this should work but I'm not able to test it with my regional settings.
Excel Formula:
=SUMIFS($B:$B,$C:$C,"Open",$A:$A,">="&DATEVALUE($G2&" 1 "&H$1),$A:$A,"<="&EOMONTH(DATEVALUE($G2&" 1 "&H$1),0))
Note that this will not work properly where the file is shared between users with different regional settings, e.g USA and UK.
edit:-
You will note that
@Toadstool and I have used different methods of identifying the month.
@Toadstool has assumed that your months are valid dates formatted as MMMM, while I have assumed that they are text names. Such details are not clear from screen captures, it is preferable that you use the XL2BB add in to post your examples as mini sheets for additional clarity (link in my signature at the foot of this post).