Answer:

Introduction:
An annulene is a cyclic compound composed of conjugated double bonds. The aromaticity of annulenes can be determined using Hückel's rule, which states that a compound will be aromatic if it possesses a fully conjugated system with 4n+2 π electrons, where n is an integer.

Aromaticity:
Aromatic compounds have unique stability due to their delocalized π electrons, which are evenly distributed over the entire conjugated system. This stability arises from the molecular orbital theory and the resonance energy associated with aromatic compounds.

[8]Annulene:
[8]Annulene has a total of 8 π electrons, making it a non-aromatic compound according to Hückel's rule. The π electron count does not satisfy the 4n+2 rule, where n is an integer. Therefore, [8]annulene is not aromatic.

[10]Annulene:
[10]Annulene has a total of 10 π electrons, which satisfies Hückel's rule. The π electron count of [10]annulene is 4n+2, where n=2. Therefore, [10]annulene is aromatic.

[12]Annulene:
[12]Annulene has a total of 12 π electrons, which does not satisfy Hückel's rule. The π electron count of [12]annulene is 4n, where n=3. Therefore, [12]annulene is not aromatic.

Conclusion:
Among the given options, only [10]annulene is aromatic according to Hückel's rule. [8]annulene and [12]annulene do not satisfy the 4n+2 rule and are therefore non-aromatic.