In the description of Fine Manipulator is written that it needs left OR right cyberhand but if I use only left cyberhand it doesn't work.
I don't have 3x3 greed tab in inventory.

The Fine manipulator works on your main hand, which defaults to right.
If you're left handed in the game option, then you'll need a left cyberarm with your left hand Fine manipulator.

For the record, the claws cyberware also obeys the same principle.