How do I solve this geometric problem?

If this is the complete question and copied correctly , you started with an erred statement

The pile would have been at 104cm before the first impact

Then use the function

104-4X = y

where X = number of impacts and y is the depth after X impacts

also , the pile will be at ground level at 26 impacts

104-4X=0 where 0 = ground level

solving for X gives you 26

I think your formula finds how far it goes on each hit, not the total depth into the ground. You need the sum of a geometric series, Sn = a1 (1 - r^n) over (1-r)

Although I looked again and it could be asking for both. The tenth one all by itself would be a(10) = a(1) times r^(10 - 1)

or a(10) = 100 (.96)^9

on the tenth impact it should be 64

because you subtract 4 each times