How to find the modulation index of an amplitude modulated signal from the spectrum analyser?
The modulation index is commonly defined as the ratio of peak voltages; the peak voltage of the message signal per the peak voltage of the carrier. Index &gt;1 causes distortion in envelope detectors, but not in synchronous demodulation.
There's comments which try to explain that unfortunately you cannot derive the time domain message signal from your coarse spectrum. You must know or guess it otherwise.
If the message happens to be sinusoidal you have already successfully calculated that the sideband peak voltage divided by the carrier peak voltage is 0.25
But there are 2 sidebands which both have 50% of the peak voltage of the signal sinewave. Thus the modulation index is 0.5
If the message is not a pure sinewave the case is complex. Do the resolution bandwidth even cover the sidebands or not? impossible to decide from the given data.  I'm afraid you must make a reference measurement and find the message amplitude which generates the same spectrum with the same analyzer settings. You, of course, must have the message signal available.