I am a newbie in this area. I answering this so that I can know whether this is a valid answer to this problem. I done this with array formula.
COUNT(IF(((MONTH(LA!$B$18:$B$44)=MONTH(DATEVALUE("01-"&$A$1)))*(LA!$C$18:$C$44=A4)),VALUE(LA!$D$18:$D$44)))