What is he empirical formula for the compound that is of 1.85 moles of nitrogen and 4.63 miles of oxygen

The empirical formula is N₂O₅.

The empirical formula is the simplest whole-number ratio of atoms in a compound.  

The ratio of atoms is the same as the ratio of moles, so our job is to calculate the molar ratio of N:O.  

I like to summarize the calculations in a table.  

Element Moles  Ratio¹   ×2²    Integers³

     N        1.85    1             2             2

     O        4.63    2.503   5.005     5

¹To get the molar ratio, you divide each number of moles by the smallest number (1.85).

²Multiply these values by a number (2) that makes the numbers in the ratio close to integers.

³Round off the number in the ratio to integers (2 and 5).

The empirical formula is N₂O₅.