SUMIF with specific date from date range



I'm trying to figure out if it's possible sum up all the mouse cages we are using at a given date. E.g. If I enter "5/20/2020", it will count the cages from study 1, 3, and 4, total of 55 cages. I tried the SUMIF formula like below but keep getting error message.

=SUMIF([Column8]8:[Column8]8, AND(Start1:Start4 <= [Column8]8, Finish1:Finish4 >= [Column8]8), [Cage #]1:[Cage #]4)

TIA for your help!


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