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The problem in your formula is caused by illogical designation of ranges. The range $G$10:$G$109 starts in row 10. Its first row is row 10. The range A$6:$A$100 has its first row in row 6.
The MATCH function returns a number, the nth row in A$6:$A$100. The criterum 3960 will be found in the range's first row. The MATCH function returns a 1.
The INDEX function applies this number to the range $G$10:$G$109 . The first row of $G$10:$G$109 is in row 10. In the formula below the range is altered to start on the same row.
[C23] =INDEX($G$6:$G$109,MATCH(B23,$A$6:$A$100,0)+4)
The MATCH function still returns a 1 but that isn't the cell you want. You want a row which is 4 rows below the one found by MATCH. Therefore the above formula adds +4. 1 + 4 = 5, and that is the cell from which the correct result is retrieved.
Your solution achieves the same result with fewer keystrokes. Some people would call it more elegant because of that which I suggest to weigh against transparency, which counts when reviewing the formula. The question that remains unanswered for me is, what is your question.
You seem to have thought of using OFFSET. By both above measures such a solution wouldn't be considered superior. For argument's sake, here it is.
=OFFSET(INDEX($G$6:$G$109,MATCH(B23,$A$6:$A$100,0)),4,0)