Question

calculate the molality of NaOH in the solution prepared by dissolving it's 4g in enough water to form 250ml of the solution.

Answer 1

Let us assume that 4 gms of Sodium Hydroxide does not occupy much volume. So volume of 250 ml is nearly that of water.  Let us assume it is diluted solution.

Weight of solvent = 250 ml * 1 kg/1000ml = 0.250 kg

Number of Moles of Sodium Hydroxide = 4 gm /(40 gm/mole) = 0.100
     as   40 is the molecular mass.

Molality = num of moles / weight of solvent in kg 
            = 0.100 / 0.250 = 0.40 Molal

Answer 2

your answer is 0.40 molar