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Yes, if you convert inches to millimetres with maths it will indeed tell you that 1/4" is 6.35 mm ....
You can come up with an equivalent number, but if the mm side of the equation is not a whole number, then it's not useful.
Not to partially side with the other guy but I have indeed gotten sets with a 6.3mm, or at least labelled as that, socket. The elusive 12.7 remains to be found.
This is interesting! Is it an imperial socket labeled in metric? Is it a specialty socket?
I never actually measured to see but if I find one soon I'll report back. Until then here's this one for sale.
I don't think you understand what everyone else is talking about so I'll tell you instead of piling on.
They're talking about socket sizes for nuts/bolts. In the US we have fractional inch socket sizes (1/4", 1/2", etc) whereas metric sockets are sized by full millimeters.
So while you are correct in saying you can convert all inch values to millimeter values, you can't always use a metric wrench on an imperial bolt, or vice versa. For example, a 6mm wrench will be slightly too small for a 1/4" bolt, and a 7mm will be slightly too large.
3/4" and 19mm just happen to be close enough to exactly the same that you can use both wrenches on either size bolt.