UK 220v 3 wire cord hookup to US 240v outlet
You can't do it, it means exactly what it says. 

The manufacturer wants "neutral" (EU blue) to be near the same voltage as ground/earth (green).  They are specifically saying DON'T do what you're trying to do, connecting line (EU brown) and neutral (EU blue) to two phases of hot (US black/red).

Transformers are your friend

A step-up/step-down transformer will do what you want.  It is an autotransformer that takes 120V hot and neutral, and gives 240V hot and neutral.  Neutrals are at the same potential.  These are packaged commercial products with the correct cords and receptacles for your market. They are heavy because they are full of copper and iron.