What is the empirical formula for the compound that has 46 grams of sodium, 64 grams of sulfur, and 48 grams of oxygen?

Your tool of choice here will be the Periodic Table of Elements.

Grab one and look for the molar mass of sodium, #"Na"#, sulfur, #"S"#, and oxygen, #"O"#. Notice that you have

#M_("M Na") ~~ "23 g mol"^(-1)#

#M_("M S") ~~ "32 g mol"^(-1)#

#M_("M O") ~~ "16 g mol"^(-1)#

This tells you that the sample given to you contains

# 46 color(red)(cancel(color(black)("g"))) * "1 mole Na"/(23color(red)(cancel(color(black)("g")))) = "2 moles Na"#

#64 color(red)(cancel(color(black)("g"))) * "1 mole S"/(32color(red)(cancel(color(black)("g")))) = "2 moles S"#

#48 color(red)(cancel(color(black)("g"))) * "1 mole O"/(16color(red)(cancel(color(black)("g")))) = "3 moles O"#

Now, in order to write the empirical formula of the compound, you must find the smallest whole number ratio that exists between its constituent elements.

Since the #2:2:3# ratio is already in its smallest whole number form, you can say that the empirical formula of the compound is

#color(green)(|bar(ul(color(white)(a/a)color(black)("Na"_2"S"_2"O"_3)color(white)(a/a)|)))#