Clearly, with a little effort, the solution that is given as correct is wrong. Just analyse the current through D1 with D2 disconnected: -
The maximum current that can flow through D1 (assuming it is ideal with zero volt drop i.e. conditions that maximize current flow), is 6 volts / 43 kΩ = 0.1395 mA or 139.5 μA.
Given that the so-called correct solution is 409 μA, it is clearly miles off.
You cannot trust the so-called "correct solution".
I would like to know where is my mistake.
I would say (given the recent history of you posting questions that supposedly have "correct answer") that your mistake is in trusting these sites or books.
Also, why did he assume that the voltage at the anodes to be zero? why
not 3 or 2 volts? How did he arrive to zero?
I've established that the "correct solution" source is faulty so there's no point trying to wonder what they did.