Each time you replace 4 qts, you end up with 1/3 new and 2/3 old oil.
Let's call the oil you want to get rid of original oil.
Since your interest is in the original oil, not the oil you just added last 4 qt change you can figure it this way...
1st 4 qt change you have 67% original oil
2nd 4 qt change you have 67& of the results of the last batch in the engine. The last batch was 67% original, so you have 0.67 x 0.67 = 0.67^2 = 0.45 or 45% old oil.
After 3 changes, 12 qts of new oil you would have 0.67^3 = 30% of the original oil.
Use 24 qts total (6 operations) and you would have 0.67^6 = 9% of your original oil left.