This part goes between the regulator and the solenoid. The 1/4 side is threaded into the regulator's 1/4 npt and the 1/8 side goes into the solenoid manifold.
This part usually goes between the solenoid and the needle valve. The male 1/8 is threaded into the solenoid manifold and the needle valve threads into the 1/8 female end.