You can do this really easy with SUMIFS because you are trying to get a number:
Formula in cell D2 from Sheet A is:
=SUMIFS('Sheet B'!$C$2:$C$8;'Sheet B'!$A$2:$A$8;'Sheet A'!A2;'Sheet B'!$B$2:$B$8;'Sheet A'!B2)
Another option would be using an array formula (it must be introduced pressing CTRL + ENTER + SHIFT ):
=INDEX('Sheet B'!$C$2:$C$8;MATCH(A2&B2;'Sheet B'!$A$2:$A$8&'Sheet B'!$B$2:$B$8;0))
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