Use a sumifs
to do this
=SUMIFS($B:$B,$D:$D,">="&G1,$E:$E,"<="&H1)
Edit: Use the following
First sumifs checks to see if a contact has started in the specified range, the second sumifs checks to see if a contact has ended in the specified range
=SUMIFS($B:$B,$D:$D,">="&G1,$D:$D,"<="&H1)+SUMIFS($B:$B,$E:$E,">="&G1,$E:$E,"<="&H1)
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