Colpitts Oscillator - Supply/Output Voltage
The question is, we give 12 V DC supply voltage to the circuit and we
get 24 Vpp output voltage what is the reason of it?

It's because the collector connects to 12 volts via an inductor. That's the short story.
The longer story requires you to think about the average voltage drop across an inductor. If the average volt drop is anything other than zero volts then the current would have to rise and rise until the inductor core saturated or the power supply collapsed.
That doesn't happen because the transistor sets the collector current to be 1 mA or 10 mA or whatever value in that sort of range. Now, because we are controlling the current through the inductor to a sensible smallish value it has to mean that the average voltage across it is zero volts.
If the average voltage across the inductor is zero volts then, the average voltage on the collector is 12 volts.
If the average voltage on the collector is 12 volts, then any AC signal on the collector has to rise equally above 12 volts in one half cycle and fall by the same amount in the other half cycle. For instance, a 2 volt peak-to-peak signal on the collector will rise up to 13 volts and drop down to 11 volts. This keeps the average voltage across the inductor at 12 volts.
So, if you pushed it, you might see a peak of 24 volts and a trough of 0 volts. If you pushed it too hard you might cause the transistor to switch off completely and you might get inductive kick-back that raised the peak voltage higher than 24 volts and, that could potentially damage the transistor. But we don't do that.