Answer
Nonbonding valence electrons means electrons present in valence shell (outermost shell) & not involved in bonding, also known as lone pairs because these are presented in pairs. Carbon has 4 electrons in its outermost shell/valence shell and all are involved in bonding and hydrogen has an electron only (atomic number- 1), so no nonbonding valence electron is present.In part
(a) sulfur with atomic number 16 and electronic configuration 1s² 2s² 2p6 3s² 3p⁴ has 6 electrons in its outermost shell third out of which 2 are bonded with carbon & another sulfur atom and 4 are presented at sulfur as two lone pairs/ nonbonding valence electrons as shown in image below.
(b) there are two atoms having nonbonded valence electrons, oxygen (atomic Number - 8) with electronic configuration 1s² 2s² 2p⁴, having 6 electrons in its outermost shell out of which 2 are bonded with carbon and 4 are presented as two lone pairs on oxygen atom and nitrogen ( atomic number - 7) with electronic configuration 1s² 2s² 2p³, having 5 electrons in outermost shell out of which 3 are bonded with two hydrogens & one carbon, remaining 2 are presented on nitrogen as lone pair/ nonbonded valence electrons.
(c) two oxygen atoms are having nonbonding valence electrons, one oxygen is same as explained in part (b), another is bearing a negative charge which means it's getting an extra electron from another atom by loosing it as positive charged ion called cation like hydrogen ion or sodium ion. So this now has total of 7 electrons from which only one is bonded with carbon and remaining 6 are presented as three lone pairs/ nonbonding valence electrons.
Work Step by Step
Note:- It's always necessary to show charge, positive or negative, on an ion like this oxygen as shown in below image (c).
Lone pair is denoted as two dots close to each other.