Which substance has the lowest vapor pressure at 75°c?
(1) water (3) propanone
(2) ethanoic acid (4) ethanol

Vapor pressure is a colligative property. This means that intermolecular forces play a large role in how volatile a substance is. We can thus assume that the substance and or liquid in this case with the strongest intermolecular forces will have the lowest vapor pressure, as intermolecular attraction will oppose the vaporizing forces created by temperature and or kinetic energy. The strongest of such intermolecular forces is hydrogen bonding, and given some knowledge of boiling point we can find the answer. In this case:
water: has hydrogen bonding, dispersion, and dipole forces for intermolecular attraction
ethanoic acid: a carboxylic acid has one polar end with a negative charge as CH3COOH turns to CH3COO-. Hydrogen bonding is also present in pure solutions.
Propanone: is a ketone and has an electronegative oxygen attached to a carbon, but does not exhibit hydrogen bonding since the O is not attached to a hydrogen. 
Ethanol: Like water exhibits hydrogen bonding, not as strong but more dispersion forces. 

Next we must understand boiling points
Water: 100˚C
Ethanoic Acid: 118˚C
Propanone: 56˚C
Ethanol: 78˚C
Given this knowledge we can order the liquids in terms of decreasing volatility or decreasing vapor pressure. We now notice that Ethanoic acid, or acetic acid will have the lowest vapor pressure at 75˚C