Step 1: Recall the link between vapour pressure and boiling point.
A liquid boils when its vapour pressure becomes equal to the surrounding (atmospheric) pressure. If the vapour pressure is lower, a higher temperature is needed to reach that pressure, so the boiling point rises.
Step 2: Recall the behaviour of the phenol-aniline mixture.
Phenol and aniline form strong intermolecular hydrogen bonds (O-H...N) when mixed, which is a negative deviation from Raoult's law.
Step 3: See the effect on vapour pressure.
Because of these strong new bonds, fewer molecules escape into the vapour, so the vapour pressure of the mixture becomes lower than expected.
Step 4: Translate to boiling point.
A lower vapour pressure means the liquid needs to be heated to a higher temperature before its vapour pressure equals atmospheric pressure. So the boiling point increases.
Step 5: Conclude.
On mixing phenol and aniline the boiling point of the solution increases (it becomes higher than that of the pure components, and the mixture can form a maximum boiling azeotrope).
Answer: The boiling point increases, because the strong hydrogen bonding between phenol and aniline lowers the vapour pressure, so a higher temperature is required to boil the solution.