You will change the percent to gram
N = 63.65 % => 63.65 g
O = 36.35 % => 36.35 g
The formula for this question is mole = mass / Molar mass
N = 63.65 g / 14.01 g/mol = 4.54 mol
O = 36.35 g / 16.00 g/mol = 2.27 mol
Take the smallest number in 2 element and divide them.
N = 4.54 / 2.27 = 2
O = 2.27 / 2.27 = 1
The empirical formula is N2O
Hope this help!