I want to do home automation project using arduino that can be control using mobile phone.
you can see the regulator fan (refer picture 1) has 6 speeds, which are 0 to 5. In picture 2, there are 6 six wires that connected to each regulator fan speed (i assumed). Is it possible for me connect all those 6 wires to arduino or other accessories that so that i can take control of those speeds using arduino. Note that, i dont have any wiring knowledge because playing with this live wire obviously dangerous. please help me.
I would leave well alone. Start with something simpler - an RGB led that you can control and then extend that. Working with mains when inexperienced is not recommended.
Agree with Pommie, thats not only a dangerous project but also that control would be hard to diy automate.
Perhaps buying an new wall unit that controlled by its own mobile App is a better option.
For other similar Mobile projects you can use your own mobile with App Inventor to an Arduino using a Bluetooth module or SMS. https://appinventor.mit.edu/explore/
It is possible, using relays to isolate the high voltage and low voltage sides of the system.
(A relay tree, one pole change over > two pole change over > four pole change over; one-of-eight output selected by three relay control signals).
However it is still dangerous and not really a good starting project.
Without a schematic for the fan controller, a wrong guess re. how it works could destroy that also.