The vapor pressure of a liquid is 0.92 atm at 60°c. the normal boiling point of the liquid could be(1) 35°c (3) 55°c(2) 45°c (4) 65°c

The answer is (4) 65°C. For this question, you need to know that the definition of boiling is when a liquid's vapor pressure equals atmospheric pressure. Normal boiling point just means boiling point at sea level, when atmospheric pressure is 1atm. For this particular liquid, you would need to raise the temperature a little for the vapor pressure to rise to 1atm (because vapor pressure increases with temperature). Therefore your temperature must be higher than 60°C, and the only such choice available to you is (4).