The important bit from the littlemachineshop page is this: ISO: CCMW060204 HSS
That is the International code for the insert. The other code, the ANSI one, is used mainly in the US, but they are complete equivalents.
The carbide equivalent of the HSS insert is CCMT060204, so any holder that will take this insert code will fit what you have.
ArcEuroTrade's own brand holders and the Sumitomo brand they also offer will fit.
This page is good for the holder codes: https://www.cutwel.co.uk/blog/learn-the-turning-tool-iso-code-system
You will need to look for something that goes SCxChyyz06 where x is the holder style, h is the hand of the holder, yy is the shank height and width and z the length. The other parts of the code are specific to the insert used, which you already have, and thus do not have a choice.
For instance, a standard, right hand turning and facing holder with a 16mm shank would be SCLCR1616H06