Thank you for uploading the model. I reviewed in the current version of the program v06.02.00.014.
In the model, ACI 318-11 is selected for the design code. For ACI, RAM Concept uses the average effective depth of the critical sections. See screen captures below showing the critical section (lengths of the perimeter section are in yellow) and output from the Auditor. The punching shear section is defined with a cover of 1.5", which corresponds to d = 4.5" and 7.5" for the 6" thick slab and 9" thick slab, respectively. The 6" slab area is roughly 8" in width.
The perimeter length is 8.13 + 7.75 + 39.5 + 15.75 = 71.13"
The effective depth is calculated as [8.13*4.5 + 7.75*7.5 + 39.5*7.5 + 7.75*7.5 + 8*4.5]/71.13 = 6.82 in
The discussion in the original forum post was associated with the AS 3600 design code. If I change the design code and then re-run the model, I see that the 4.5" (the thinnest effective depth) is used in the calculation: