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why sulfur can make more bonds than oxygen

I am confused that the answer to this question:

Which of the following best explains why sulfur can make more bonds than oxygen?

The answer is that Sulfur has 3d orbitals not available to oxygen. I am confused because I know the electron configuration is [Ne] 3s2 3p4 and does not include the d orbital.

Hybridization theory is used to explain this. 

Normal chemical bonds take place as a result of the overlap of 1/2 filled orbitals.  In the case of oxygen, there are two half filled orbitals in the 2p subshell that can overlap.  In water they overlap with the half-filled s orbitals in two hydrogen atoms.

However, if we look at Carbon, that normally forms 4 bonds despite the fact that it contains only 2 half-filled orbitals in the p subshell.

Hybridization theory is used to explain why this happens.  According to this theory one of the electrons in the filled 2s orbital is "promoted" to the empty 2p orbital.  This promotion results in the formation of 4 equal orbitals (called sp3 hybrid orbitals).  Each one of these hybrid orbitals is 1/2 filled and capable of forming a bond, thus explaining why C atoms regularly form 4 bonds.

Hybridization theory is also used to explain why sulfur is able to form 6 bonds in compounds like SF6.  In this case electrons are "promoted" from the filled 3s and 3p orbitals to form 6 1/2 filled orbitals (called sp3d2 hybrid orbitals).  These 6 1/2 filled hybrid orbitals are then able to overlap with the single 1/2 filled 2p orbital in each of the 6 F atoms.