The easiest way to think about this is the following: look at the electron-domain geometry about the central atom in the molecule. We will need as many hybrid orbitals as there are electron pairs around the central atom. The sp hybrid set contains 2 orbitals, the sp2 set 3, the sp3 set 4 orbitals, and so on.
From the Lewis structure, the central Si atom has 4 electron pairs. The hybrid orbital set which contains 4 orbitals arranged in this way is the sp3 set.
The Lewis structure has the C atom sharing three pairs (a triple bond) with the N and one pair with the H. Therefore the central C atom is surrounded by two electron pairs, and it is using the sp hybrid set.
We have 24 electrons to place in the Lewis structure; the central S atom forms one double bond and 2 single bonds (there are resonance forms but they do not change the hybrid orbital set.) We have three electron pairs around the S atom; the hybrid set is sp2.
We have 22 electrons in the Lewis structure; the central I atom has two bonding pairs and three nonbonding pairs for a total of five pairs. The hybrid orbital set which contains five orbitals is the dsp3 set. Would the lone pairs be oriented axially or equatorially to minimize repulsion?
There are 36 valence electrons to place; the central Br atom is surrounded by six electron pairs, and is using the d2sp3 hybrid set.