Explanation:

- A 3c-2e bond refers to a bond in which three atoms share two electrons. This type of bond is commonly found in compounds containing boron, beryllium, and aluminum.
- Option 'A' is BeH2 (dimer), which has two BeH2 molecules bonded together through hydrogen bonds. Each BeH2 molecule has four electrons in its valence shell and forms two 2c-2e bonds with the two hydrogen atoms. Therefore, there are no 3c-2e bonds in this compound.
- Option 'B' is BeH2 (solid), which has a repeating crystal lattice structure. Each Be atom forms two 2c-2e bonds with the two neighboring H atoms, and there are no 3c-2e bonds in this compound.
- Option 'C' is C2H6, which is ethane. Each carbon atom forms four 2c-2e bonds with the four hydrogen atoms, resulting in a total of eight electrons in the valence shell. There are no 3c-2e bonds in this compound.
- Option 'D' is B2H6, which is diborane. Each boron atom forms three 2c-2e bonds with the three neighboring hydrogen atoms, resulting in a total of six electrons in the valence shell. There are two 3c-2e bonds in this compound, which account for the unusual bonding and reactivity of diborane.

Therefore, the correct answer is option 'C' because it does not have any 3c-2e bonds.