The vapor pressure of a solvent is a colligative property. That means that it depends on the number of particles of the solvent in solution and not the nature of the solute dissolved.
You have to use Raoult's law, which states that the vapor pressure of a solution is equal to the vapor pressure of the pure solvent times the molar fraction of the solvent, i.e.:
P = P°solv * X solv
X solv = number of moles of solvent / number of moles of solution
solvent = water
solute = glycerin
number of moles of water = mass of water / molar mass of water
number of moles of water = 1000 g / 18.02 g/mol = 55.49 mol
number of moles of glycerine = mass of glycerin / molar mass of glycerin
number of moles of glycerin = 180g / 92.09 g/mol = 1.955 mol
X solv = 55.49 mol / (55.49 mol + 1.955 mol) = 0.966
P = 23.8 torr * 0.966 = 22.99 torr = 23.0 torr
=> Vapor pressure lowering = 23.8 torr - 23.0 torr = 0.8 torr
Answer: 0.8 torr.