The brightness of light bulbs in this circuit
Whomever wrote that answer is an idiot. Clearly, bulb b must get brighter since, with the pot at x, the bulb is shorted out and must be dark.

As for bulb a, it must get brighter. At x, you have the resistance of the pot in series. At y, bulb b is in parallel with the pot, reducing the series resistance.

Edit: typo