Stability order of octahydrobiphenylenes
While solving other related questions, I came up with a idea that 


  More is the number of $\alpha$ hydrogen present(hydrogen attached to carbon which is adjacent to a carbon containing double bond ) more stable is the compound.


In the question $Z$ has maximum 10 $\alpha$ hydrogen so it is the most stable.$X$ and $Y$ both have 8 $\alpha$ hydrogen.But $Y$ is more stable since conjugated double bond in short non aromatic cyclic system is highly disfavoured. 

Hence the correct stability order is $Z&gt;Y&gt;X$

Side note- I am still not satisfied with my second argument.Any other explanations or thought will be highly appreciated.