Zeus Charts give 6-32 ANC as having an OD of 0.138", and 8-32 as 0.164" The thread form will be 60 degrees
There is no ANF thread with 32 tpi pitch.
It could be 10-32 UNF which is 0.164" diameter, but slightly truncated to give the 0.158" OD.
If it were 4mm it would be 0.15748" diameter, but M4 is 0.7mm pitch which is 17.78 tpi.
HTH
Howard