Double bond equivalent (degree of unsaturation) of (A) is :
Let us first deduce the structure of A. The given reduction (hydrazine is a decent clue), selectively reduces symmetrical C=C bonds via the formation of diimide - HN=NH. Usually, this method works for alkynes, allenes and unhindered alkenes. In this case, the given alkene seems sterically hindered and hence diimide reduction will indeed be hardly effective. But still, there are no other clues and given the nature of the problem, so we assume it is the reduction of an unsaturated hydrocarbon (because diimide reduction does not affect polar C=O C=N bonds). So this has to be the substrate (there can't be a triple bond). Also, this type of hydrogenation is syn in nature - meaning, the product, in general, is cis .
There are two rings and a double bond. Hence DOU or DBE = 2 + 1 = 3