The portable dishwasher attaches to your faucet with an aerator. This aerator is spring loaded against a cardboard retainer. When installing the aerator, this retainer should be removed. Hold down the rubber o-ring when removing the retainer to keep the assembly from coming apart. Should the assembly come apart during installation, assemble the aerator as shown below, and then attach it to the faucet.
The adapter is not needed in all installation applications. The adapter is used only if you have internal threads on your faucet.