Lewis structure of SI6 is this as you know :
http://www.chem.purdue.edu/vsepr/index_files/SI6.bmp

My question is , how come that S , can be connected to 6 Iodine molecules, (which means S, is connected to 12 electrons instead of 8 ), while S needs only two electrons to reach an octet?

Sulfur can hybridize its orbitals to form more than just four bonds.
Does SI6 exist?

I would say surely DrBob :)

You perhaps know (or will learn maybe soon) that electron shells consist of orbitals, the s, p, d and f orbitals.

The first electron shell contains only s orbital, the second shell contains s and p orbitals, the third, s, p and d while the fourth and above contain all of s, p, d and f. Since the last electrons of sulfur are in the third shell, you have the s, p and d orbitals available. S can contain 2 electrons, p can contain 6 electrons and d can contain 10 electrons, for a total of 18 electrons!