Answer
$13.83\%$
Work Step by Step
Number of moles of the red solid:
$0.206\ g\div288.915\ g/mol=0.000713\ mol$
From stoichiometry, that's the same number of moles of nickel (II) nitrate and NiS
$0.000713\ mol\times 90.758\ g/mol=0.0647\ g$
Mass fraction:
$0.0647\ g/0.468\ g\times100\%=13.83\%$
