With your sample data in columns A thru F and rows 1 thru 3, I arrived
at 2 solutions: one using an array function and another using
sumproduct. User entry is in cell I1.

The array function is
=SUM(IF(I1=A1:E3,F1:F3,0)) (Invoke the array function by
simultaneously pressing CTRL-SHIFT-Enter)

The Sumproduct answer is
=SUMPRODUCT(--(I1=A1:A3),F1:F3)+SUMPRODUCT(--(I1=B1:B3),F1:F3)+SUMPRODUCT(--(I1=C1:C3),F1:F3)+SUMPRODUCT(--(I1=D1:D3),F1:F3)+SUMPRODUCT(--(I1=E1:E3),F1:F3)