restore PT3 database on PT4

[Jeffrey]

How do I get all my hands from my PT3 database to my PT4 database and vice versa?

Is there maybe a way that both systems could update once in a while those databases?

I have PT3 on my macbook and PT4 on my pc. Would be nice if there was a way they could synchronize.

[WhiteRider]

The databases are completely separate so you can't "restore" them either way.
PT4 has a mechanism to convert a PT3 database, but once you're set up with both databases the easiest way is to import the hand history files into both. Check out the Tutorial: Synchronizing Databases - this was written just for PT3 but the same principals apply here.