If molality of the dilute solution is doubled, the value of molal depression constant ($K_f$) will be:

The molal depression constant ($K_f$), also known as the cryoscopic constant, is a characteristic property of the solvent only. It depends on the molar mass, boiling/freezing point, and enthalpy of fusion of the solvent. It does not depend on the concentration (molality) of the solute.