I wanna build a circuit with different output voltage from 12V->9V->6V->5V. When i build the circuit like 7809 voltage regulator, it require 3 capacitor to get 9V output. After i get the 9V output, was it necessary to build a 6V output with 7806 and 2 capacitor or without capacitor ? Same concept applied for the 7805 as well?
Why don't you look at the datasheet for a 78xx voltage regulator IC? It explains why an input capacitor and an output capacitor are needed.
Usually a voltage regulator IC does not need the 100uF capacitor on its output.