A scientist or technician working with (or developing) a device, transport, or portal, by accident or for reckless-research inserted his hand into the "active" area (perhaps located between two poles), causing it to be rotated through higher dimensions (?), and for the duration, or perhaps permanently, leaving him with two right or two left hands. - (Online searches only returned references to various 1920s short stories, and Kant.)
This is one of the two blurry ancient mental images we could not identify after a discussion of old SF or weird tales (most likely) from a late 20th-century childhood of US broadcast television. If so, probably from syndicated series, or independent station afternoon or late-night programming (which could include an occasional UK, or english-language dubbed european or japanese production) - and much less likely something animated (because of the subject matter).