Without hyperfine interaction:
The exercise mentions g=1 but does not define which g and the picture mentions g_J=0.8. 0.8 was used.
with hyperfine interaction
Correction on terms:
Former m_J=-3/2 -> -1/2:
Obviously something is wrong here and I suspect it stems from my lack of understanding regarding calculating the hyperfine correct. I addressed this while watching in one of the questions I sent.