the sulfur has 2 atoms bonded (the H) and 2 pairs of electrons, which is a total of 4 electron domains. The hybridization of the sulfur therefore is sp3

Nitrogen is a Group 5 element, so when it is bound to three hydrogen atoms, it will have a lone pair.

\(\displaystyle NH_3\) has four areas of electron density (three bonds and one lone pair), so its bonds are \(\displaystyle sp^3\) hybridized.

Because of the lone pair, \(\displaystyle NH_3\) has a trigonal pyramidal geometry.

\(\displaystyle sp^{2}\) hybridization occurs when a double bond is present in a molecule. The only molecule that has a double bond is ethene \(\displaystyle (C_{2}H_{4})\). Both carbon atoms exhibit \(\displaystyle sp^{2}\)hybridization.

\(\displaystyle sp^3\) hybridization is observed in atoms that have only single bonds, while \(\displaystyle sp\) hybridization occurs when a triple bond is present. The other given molecules all contain only \(\displaystyle sp^3\) hybridized atoms.

Carbon hybrid orbitals are combinations of s and p valence orbitals, and are equal in energy. The hybridization of an atom is dependent on the number of atoms that it is bonded to, as well as the number of lone pairs on the atom in question. A carbonyl carbon is bonded to three other atoms (keep in mind the double bond is not counted twice!) and it has no lone electron pairs. As a result, a carbonyl carbon will exhibit \(\displaystyle \small sp^2\) hybridization.

A carbon with four substituents will be \(\displaystyle sp^3\) hybridized. A carbon with a double bond will be \(\displaystyle sp^2\) hybridized. A carbon with a triple bond or two double bonds will be \(\displaystyle sp\) hybridized.

Trigonal bipyramidal geometries arise from the hybridization of one s orbital, three p orbitals, and one d orbital, hence the name \(\displaystyle sp^3d\).

Each s subshell has 2 electrons in it, each with opposing spin. 

Each p subshell can have a maximum of 6 electrons in it. Note that there are three p orbitals, denoted p_x, p_y, and p_z. These orbitals represent the plane in space in which they reside.

Remember that the d block involves the transition metals. There are 10 transition metal elements per row/period, and those 10 transition elements represent the maximum 10 possible electrons that can be held per d subshell. The d subshell has five orbitals, each with the potential to hold two electrons.

The f block includes the lanthanides and actinides. There are 14 elements per period/row in the f block, which represent each electron that can fit in the f subshell. Thus the f subshell has seven orbitals, each of which can hold a maximum of two electrons for a total of 14.

Remember, the energy level number is equal to the row number on the periodic table. Looking at row 1, s is the only subshell possible in this row. It has a maximum of two electrons.