I'm on the confused team with vector doctor. The way the op was worded, it sounded like you needed the body of the letters to be a uniform 6mm, i.e. no portion of the letter being wider or narrower than 6mm. Like the W in ops post, the "wing tip" on the left of the is wider than the "wing tip" on the right. In the Vector Dr.'s sample below that the "wing tips" are a uniform width. After a few posts it seems OP might want to simply add a uniform 6mm around the existing lettering as it is.
In either case, the good Doctor is 100% correct in how to proceed.
If his first interpretation is correct, you would want to redraw each letter with a single stroke in the middle at 6mm and round the caps. This will give you the uniform width letter body like my sample on the left
If it was the latter, then his instructions to offset the path would give you results like my example on the right.