In the DEPT 90 appears just carbon atoms bound to one hydrogen atom, and all signals have to be up
In the DEPT 135 appears all carbon atoms bound to hydrogen atoms. Completely unsaturated carbon atoms don't appear. Carbon atoms bonded to two hydrogen atoms must appear down.
As this structure has a symmetry plane, let's count the signals just of one side of the symmetry plane because every specular atom has the same chemical environment, so they will have the same signal. So:
In DEPT 90 we should expect to see 6 up signals.
In DEPT 135 we should expect to see 8 signals, not 9, because the two -CH3 in the isopropyl group are chemically identical, they will have the same signal. And all signals must be up because this structure doesn't any carbon atom bound to two hydrogen atoms.
The correct option is the third option.
The correct answer is the first option.
This question is about the hydrogen atoms in bold letters in the figure above. These hydrogen atoms appear in an RMN-1H around 7-8 ppm because they are less protected than hydrogen atoms in sigmaC-H. Circulating π electrons in the conjugate cycle caused a "ring current" which has a magnetic field. In the outer parts of the ring, this magnetic field will reinforce the magnetic field generated by the instrument. So, these hydrogen atoms suffer a higher magnetic field magnitude than other hydrogen atoms in the molecule.