The word amphoteric means dual nature. Therefore, an amphoteric oxide is a molecule that has the properties of both acid and basic oxides. These molecules can react with both acids and bases to form salts and water. 

The amphoteric oxide exhibits such dual characteristics due to its oxidizing state. In general, amphoteric oxides belong to Group 2-alkaline earth metals and transition metals.
Now let's take a look at the options given to us.
1. The first molecule given to us is ${\mathrm{Cr}}_2{\mathrm{O}}_3$. This molecule has +3 oxidized chromium. It is essentially amphoteric as Cr is a transition metal. Chromium can reach both lower and higher oxidation states. This compound reacts with both acids and bases to form salts and water. Therefore, ${\mathrm{Cr}}_2{\mathrm{O}}_3$ is amphoteric.
2. The next molecule given is $\mathrm{BeO}$. This Be has a higher electronegativity than lithium, and the Be-O bond is essentially a covalent bond. This molecule is at the acid-base boundary. Therefore, it shows the behavior of both acids and bases. Hence, $\mathrm{BeO}$ is amphoteric.

3.  The 3^th molecule is $\mathrm{SnO}$. Tin oxide is also amphoteric because it can form both water and salt with acids and bases.
4. The fourth molecule is ${\mathrm{SnO}}_2$. ${\mathrm{SnO}}_2$ reacts with both acids and bases to form water and salts. Therefore, it is also amphoteric in nature.
5. The next molecule is $\mathrm{CrO}$. This oxide is basic in nature and chromium has a +2 oxidation state.
6. Then the other molecule is $\mathrm{PbO}$. Lead oxide is essentially amphoteric because it can react with both acids and bases to form salts and water.
7. The next molecule is $\mathrm{ZnO}$. Zinc oxide is also amphoteric in nature and reacts with acids and bases to form both salts and water.
8.The next molecule is ${\mathrm{Al}}_2{\mathrm{O}}_3$. This aluminum oxide is also amphoteric in nature.
9. Next is ${\mathrm{PbO}}_2$. This is also Amphoteric. 

10. The $\mathrm{NO}$ molecule is a neutral oxide. Such oxides do not exhibit the properties of acidic and basic oxides.
11. The ${\mathrm{B}}_2{\mathrm{O}}_3$ molecule is actually anhydrous. It reacts with water to form boric acid, which is inherently acidic. Therefore, it is classified as an acid oxide.

Hence, all the molecules of options A and C are amphoteric in nature.