The concentration of the kcn solution given in part a corresponds to a mass percent of 0.473 %. what mass of a 0.473 % kcn solution contains 748 mg of kcn?

If the Ka of HCN = 5.0 x 10^-10
Since
(Ka) (Ka) - 1 x 10^ -14
then
the Kb of its conjugate base (CN-) = 2.0 X 10^-5

since
pH + pOH = 14
when the pH = 10.00
then
the pOH = 4.00
& the OH-
would then equal 1.0 X 10^-4

NaCN as a base does a hydrolysis in water:
CN- & water --> HCN & OH-
notice that equal amounts of OH- & HCN are formed

Kb = [HCN] [OH-] / [CN-]

2.0 X 10^-5 = [1.0 X 10^-4] [1.0 X 10^-4] / [CN-]

[CN-] =(1.0 X 10^-8) / (2.0 X 10^-5)

[CN-] = (5.0 X 10^-4)

that's 0.00050 Molar
which is 0.00050 moles in each liter of aqueous KCN solution
which is
0.00025 moles KCN in 500. mL of aqueous KCN solution

use molar mass of KCN, to find grams:
(0.00025 moles KCN) (65.12 grams KCN / mole) = 0.01628 grams of KCn

which is 16.3 mg of KCN
& rounded to the 2 sig figs which are showing in the Ka of HCN , "5.0" X 10^-10
your answer would be
16 mg of KCN

sorry even after making a correction in calcs , I don't get one of your answers.
the only way that I could get one of them is to pretend that yours was a 1 sig fig problem,
in which case your 16 mg would round off to 20 mg.
but you have 3 sig figs in "500. ml", & 2 sig figs in both the "pH of 10.00."
& The Ka of HCN = "5.0 x 10^-10."

it does however take 12 mg of NaCN, to make 500. mL of aqueous solution pH of 10.00. the molar mass of NaCN has the smaller molar mass of 49.00 grams per mole.
maybe they meant NaCN, but wrote KCN instead.

I hope i answered this correctly for you.