The molality is 0.50 mol/kg.
molality = #("moles of [solute](//socratic.org/chemistry/solutions-and-their-behavior/solute)")/("kilograms of [solvent](//socratic.org/chemistry/solutions-and-their-behavior/solvent)")#
moles of NaOH = 10 g NaOH × #(1"mol NaOH")/(40.00"g NaOH")# = 0.25 mol NaOH
kilograms of H₂O = 500 g H₂O × #(1"kg H₂O")/(1000"g H₂O")# = 0.500 kg H₂O
molality = #("moles of solute")/("kilograms of solvent") = (0.25"mol")/(0.500"kg")# = 0.50 mol/kg