Dear Student
In HNO3 , the oxidation state of Nitrogen, N is:
[+1 + (x) + (3 * (-2))] = 1 + x - 6 = x - 5
Therefore, x = +5
Now, according to the question, 4 moles of e- are transferred to 1 mole of HNO​3
which means that the oxidation state of Nitrogen, N will get reduced by 4
Thus, the oxidation number of N becomes, x = 5 - 4 = +1
Thus, the possible reaction would be:
HNO​3 -------> 0.5 N2O
(+5) ----------> (+1) (2) [=+1]
Regards