How does the valence of non-metals increase?

Valence is the ability of atoms to attach to themselves a certain number of other atoms. There are elements that have constant valence:
1) the atoms of the first group are monovalent (I), these are H, Li, Na, etc.
2) the atoms of the second group are divalent (II), these are Be, Mg, Ca, Zn, etc.
3) the atoms of the third group are trivalent (III, these are B, Al, Ga, etc.
The highest valence of non-metals is equal to the number of their group.
The lowest valence is equal to the difference between the number 8 and the number of the group in which the non-metal is located.