To find the pairs of shared electrons in a covalent bond, you first have to know the formula of the substance, as well as the number outermost shell electrons of the constituent elements.
In chlorine, since chlorine atom itself is very unstable, it has to form a molecule by itself. The formula of chlorine gas is Cl2. 2 chlorine atoms are bonded together. So, since Cl atom has 7 outermost shell electrons (can be found by the group of the element), they need 1 more electron in order to have the octet of electrons (8 outermost shell electrons, where they're the most stable).
Therefore, if each of the Cl atom shares one of their electrons to other, they'll both have one extra e-, which makes them stable, so, the answer to the first one is 1 pair.
Using the same steps, we can find all the answers to the questions.
Nitrogen, formula is N2. Each N atom has 5 outermost shell electrons, thus each need 3 more to become octet. Each N atom shares 3 so they gain 3 from the other N atom. The no. of pairs is 3.
Water, formula is H2O. Note that in this structure, both H atoms forms a covalent bond in the same O atom, but not forming with each other. H has 1 outermost shell e-, and 6 for O. Special case for H, they only need 2 electrons in total in the outermost shell in order to become stable (bc it's their 1st shell). So, each H atom shares 1 e- with O, so that each H can gain 1 e- to become stable, and O gains 2 more e- from H to have 8 in the shell. So, the in total, there is 2 pairs, but only 1 pair for each H and O atom.
Carbon dioxide, CO2. Carbon needs 4 more e- to become stable, while 2 for each O atom. So, each O shares 2 and gains 2, while carbon gains 4 when it shares 2 e- for each O atom. So, in between each C and O atom, there should be 2 pairs.
Ammonia, NH3. Again, each N atom needs 3 e- to become stable, while 1 for each H atom. So, the 3 H atom each shares 1 to N, while N shares 1 to each of them. Thus, the no, of pairs between each N and H atom should be only 1.
Methane, CH4, very similar to ammonia, where each C atom needs 4 e- to become stable, while 1 for each H atom. So, each H atom shares their 1 to C, while C shares its 4 e- to the 4 Hs to become stable. Therefore the no. of pairs between each H and C should be only 1.
