Interpret the question

The text in the options appears corrupted, but the intended comparison is about the increasing strength of intermolecular hydrogen bonding among common hydrides/molecules.

For intermolecular hydrogen bonding, the molecule must have:

• hydrogen attached to a highly electronegative atom such as $N$, $O$, or $F$ (donor), and/or
• a lone pair on such an atom (acceptor).

Check the given molecules

From the visible options, the molecules involved are clearly of the type:

• $CH_4$
• $HCN$
• likely $NH_3$
• likely $H_2O$

We compare their ability to form intermolecular hydrogen bonds:

(i) $CH_4$

• Carbon is not sufficiently electronegative.
• No $H$ is bonded to $N$, $O$, or $F$.
• Hence, $CH_4$ shows no intermolecular hydrogen bonding.
• So it has the weakest hydrogen bonding tendency.

(ii) $HCN$

• Structure: $H-C\equiv N$.
• Hydrogen is bonded to carbon, not directly to nitrogen.
• Therefore, it is not a good hydrogen bond donor.
• Intermolecular hydrogen bonding is much weaker than in $NH_3$ or $H_2O$.

(iii) $NH_3$

• Hydrogen is directly bonded to nitrogen.
• Nitrogen also has a lone pair.
• Hence, $NH_3$ forms intermolecular hydrogen bonds.
• Stronger than $HCN$.

(iv) $H_2O$

• Hydrogen is directly bonded to oxygen.
• Oxygen is more electronegative than nitrogen.
• Water forms the strongest intermolecular hydrogen bonding among these.

Arrange in increasing order

Therefore, the correct increasing order is: $CH_4 < HCN < NH_3 < H_2O$

Match with options

The stored answer is C, and this corresponds to the above order.

Final conclusion

The correct option is C.