You shouldn’t really play about with mixing up metric and imperial threads on the same job, as metric is defined by pitch (the amount the screw moves forwards in one full revolution) and the imperial system of threads per inch (TPI).
But when attempting to find a somewhere near compatible metric thread for replacing an imperial one, it is fairly easy.
Divide 25.4 by the pitch of the metric thread.
So for a 6mm course (1mm pitch) = 25.4÷1= 25.4TPI
and
6mm fine (0.75mm pitch) = 25.4 ÷0.75=33.8TPI
So looking at the results, the 6mm fine pitch would be a fairly good replacement for
1/4″ x 32TPI.
Normally, the main reason for all the different pitches and TPI’s is actually to do with the strengths of the parent metals.
You would use a coarser pitch in softer materials as there would then be less risk of stripping the threads.
You also have to be aware that most imperial threads have a 55º thread angle whereas metric and the US system use a 60º angle, then you come to the famous BA system which for some reason uses 47.5º.
I hope this has helped to clear up a few points, and I am sure there will be some who can make it as complicated as you would ever want.
Bogs