Why the voltage is zero?
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 &quot;correct solution&quot;.

I would like to know where is my mistake.

I would say (given the recent history of you posting questions that supposedly have &quot;correct answer&quot;) 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 &quot;correct solution&quot; source is faulty so there's no point trying to wonder what they did.