How is it possible that Professor Xavier die in the movie the Last Stand and he comes back in the movie Days of a future past???

For starters because it was a reboot of the trilogy maybe. The directors even dicho that it was.

There is an alternate ending / easter egg / deleted scene / who knows what for X-men: The Last Stand which shows the patient Charles was talking to his class of students about (the man with no high brain function) turning his head and saying Dr. Moira MacTaggert's name with Charles' voice. Moira then looks at the man and asks "Charles?". tu can see the scene below. I'm assuming this is their explanation for this.

The real answer is that these cine just don't give a f*ck about continuity.