=SUMPRODUCT((TEXT(LA!$B$3:$B$44,"mmm")='Resource Monthly'!$A$1)*(LA!$C$3:$C$44='Resource Monthly'!$A4))
or little bit longer but faster than above formula..
=COUNTIFS(LA!$B$4:$B$44,">="&1&'Resource Monthly'!$A$1,LA!$B$4:$B$44,"<="&EOMONTH(1&'Resource Monthly'!$A$1,0),LA!$C$4:$C$44,'Resource Monthly'!$A4)