To put it where you want it, it has to be the same size and thread on both sides, since you're inserting it into an existing connection.
From the diagram, if you bought the right size unit, they expect you to use the adapter ring to fit one side it the other, depending on whether your existing fitting is 1/2" or 3/8". The adapter should either screw into the hose or onto the valve.
If it doesn't fit either way I'd say you have the wrong version of this add-on valve and need to figure out what size you pipe fittings actually are are. Something metric?