What is the weight/weight % of 9.74g of sodium sulfate to a final volume of 165 mL of solution?

The problem here is that you're missing the density of the solution, which implies that you cannot use its volume to determine its mass.

The solution's percent concentration by mass, `"% m/m"`, tells you the number of grams of solute present for every `"100 g"` of the solution.

You know that the solution contains `"9.74 g"` of sodium sulfate, but you don't know its total mass, so you can't determine how many grams of sodium sulfate you'd get for `"100 g"` of this solution.

Now, let's say that this solution has a density of `rho quad "g mL"^(-1)`, which implies that you get `rho quad "g"` for every `"1 mL"` of the solution.

In this case, the total mass of the solution will be

`165 color(red)(cancel(color(black)("mL solution"))) * (rho quad "g")/(1color(red)(cancel(color(black)("mL solution")))) = (165 * rho) quad "g"`

So now that you know that you have `"9.64 g"` of sodium sulfate in `(165 * rho) quad "g"` of this solution, you can say that `"100 g"` of the solution will contain

`100 color(red)(cancel(color(black)("g solution"))) * ("9.64 g Na"_2"SO"_4)/((165 * rho) color(red)(cancel(color(black)("g solution")))) = (5.84 * rho) quad "g Na"_2"SO"_4`

This means that the solution's percent concentration by mass is equal to

`"% m/m" = (5.84 * rho)% quad "Na"_2"SO"_4`

So if you find the density of the solution, you can plug in its value and get the solution's percent concentration by mass.