Twinned spell is part of a specific spell action...
Now i Will simplify it to explain Why it you cant twin the melee of booming Bode
An action
When casting a spell you dont use your action unless the casting time is the same as an action... i hope we Can agree on this...?
Yes.
When casting booming blade for it to work just one melee attack is needed - hope we Can agree on that?
Normally, yes. But Twinned Spell changes how spells work, or at least that is one way to read it. The description of Twinned Spell says that you get to "target a second creature in range with the same spell." In my previous post, I asserted that the way to read this is that Twinned Spell causes the single casting of the spell to target two creatures. In this case, the only reasonable thing to do is to extend the spell in the most straightforward way to accommodate targeting two creatures. In the case of Booming Blade, this would be to make a melee attack on each of the two creatures.
However, on reflection, I think it is better to read Twinned Spell as effectively allowing you to cast the spell twice with the same action, targeting two different creatures. Not only is this more consistent with the name "Twinned Spell", but it also makes the interpretation much easier since you leave the spell description itself unchanged.
Using this reading, I can agree with you - each casting of Booming Blade requires just one melee attack. But applying Twinned Spell essentially causes you to cast the spell twice with the same casting action, so you will end up making two melee attacks - one for each casting.
Booming blade melee attack requires to be part of your action used regardless if its spell casting or whatever you wanna put it under... the melee attack still requires to be part of your action... we Can agree on this?
Yes.
If we Can agree on these terms... its Per default from rules of mechanics impossible to twin the melee part.
As much as I appreciate your effort in trying to explain your opinion on this, I'm sorry, but I don't understand which 'rules of mechanics' are you referring to? If you could
cite a specific passage in the PH or Basic Rules or other source, that would be very helpful in understanding what you are talking about.
If, though, your argument still comes down to the assertion that two melee attacks cannot be part of the same action, that's just not correct. As I noted previously, there are plenty of examples in which multiple melee attacks result from a single action.
That Said it doesnt stop the spell from being Twinned.
Also it Can be read on the Way you descripe where the attack is magical and some ghost sword hits the other target simultaniously (even though that wouldnt be a direct twin spell since you dont create some kind of ghost sword in the first place). Problem here is that the rules of magic attacks apply and is directly against the text of how the melee attack works within booming blade cause it would State its a regular effect and not magical. But if we Can twin cast the melee it has to be magical and Thereby magic effect has to apply according to the rules right? Or do you wanna avoid the rules of magic too?
Again, what rules are you referring to? And why do you think they conflict with the Booming Blade spell description?
EDIT: Oops, this is now redundant with what others have said already.