seledeur said:
Actually I'm just a high school student, I don't understand ' -6 dB/octave (-20 dB/decade' , and I still don't get why can't we have fs >> Fp ? or maybeif fs is too big, we don't really need modulation ?
Oh, this is high-school. I'm impressed!

Okay, never mind about the -6 dB per octave thing or the details of filter design (unless you've already covered RC circuits).
Back to the definitions in the original problem statement.
Fp is the frequency of the Carrier
fs the frequency of the original signal
At the very least it's obvious that Fp must be greater than fs, by plotting the modulated signal's power or amplitude as a function of frequency (i.e., by plotting its spectrum).
Plot the original signal's unmodulated spectrum, with frequency on the horizontal axis and power spectral density (or singnal amplitude density) on the vertical axis. Don't forget negative frequencies. Zero Hz is right in the middle, with negative frequencies on the left and positive frequencies on the right.
Don't worry if you don't know the true shape of the original signal. Just make something up. Suffice it to say it has some sort of a shape in positive frequencies, with a peak frequency. The negative frequencies are a mirror image of the positive frequencies.
Now draw the power spectral density (or amplitude spectrum density) of the modulated signal, where the original signal is "shifted up the dial" so to speak, by the carrier frequency, Fp. Something like this (with different variable names):
Now ask yourself what would happen if the orignal frequency's peak frequency was greater than the carrier frequency? What would the spectrum of the modulated signal look like then? Would it not overlap with itself?
That explains why the carrier frequency must be
greater than the peak frequency of the original signal. But why must it be
much, much greater (">>") as opposed to just
greater (">")? The only things I can think of are practical reasons I brought up earlier, such as filter rolloff requirements and antenna length. Other than practical concerns, the carrier frequency only needs to be "
greater"; not
much, much greater; than the original signal's frequency. Other than that, you might want to skim through your coursework again and see if the material hints at anything more specific [I can't think of anything else].