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The 6 in '6-32' refers to "machine screw size no 6".

From that you can get to a "tap/drill size chart" such as this.

That particular chart says is should be a "no.36" drill, or  0.1065" (~2.7mm)

But these sizes are for tapping, something you should be doing if you are using the screws shown in the picture, as they are not always very good quality, and can snap if you don't.

If you want to just "screw it together" then something like this self tapping screw with a suitable washer might be more suitable, but be careful with the pointy bit.

 

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Yeah. it's either UNC 6-32  (imperial, 32 threads per inch)   or M3 (metric, 3) which was used for optical drives. Majority of cases use UNC 6-32 screws.

 

The typical length (from screw head) is most likely 0.25" (6.35 mm) for unc 6-32 screws.

 

 

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the drill bit you would need would depend on the material you plan on using the screw in.. the screw in the pic is a standard case screw usually for holding the PSU to the case which brings up the other point in what is the screw going to be securing. if its like a PSU then the size doesnt matter too much but its better to go slightly smaller. for instance the linked chart that Ralphred provided says this screw is

 

Thread Size    Tap-Drill Sizes    Clearance Holes
Size    DIA    Close Fit    Non-Struct (1/64 OS)

6-32-UNC    No. 36    .1065    No. 28    No. 23 or 5/32

 

on a tap and dye set the numbers you would be looking for are 36, 28 and 23.

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