Freezing point depression.
∆T = imK
∆T = change in freezing point = 68.88º - 63.6º = 5.28º
i = van't Hoff factor = 1 if the unknown doesn't ionize or dissociate. They don't mention the nature of the unknown so we'll have to assume the value of i to be 1. This is a poorly written quesiton.
m = molality = moles solute / kg solvent= ?
K = freezing constant = 4.50º/m
5.28 = (1)(m)(4.50)
m = 1.17 m (the fact that 1.00 g is dissolved in 9.116 g does not enter into the calculation, unless you wanted to determine the molar mass of the unknown)
[What a strange question, for sure!]