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The N2H2 structure does not have resonance because there is only one Lewis structure that satisfies the octet rule for N and also uses the 12 valence electrons in the molecule. If you remove one lone pair from each of the Nitrogen atoms to create a triple bond between them, the resulting Lewis structure would have 10, not 12, valence electrons. To determine whether a molecule has resonance, you would check the Lewis structure and see whether or not a lone pair can be used to create a bond while simultaneously using the total number of valence electrons in the molecule. In the second picture you posted, there is resonance because one of the lone pairs on the N atom was used to create another bond between N and C (and it did not change the number of valence electrons in the molecule). Therefore, there is resonance in that molecule.
to check whether a molecule has a resonance or not, draw the lewis structure and see if you can find multiple possibilities that satisfy the requirement. N2H2 doesn't have a resonance structure because there's only one way to meet all the requirements.
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