The solution in the flask is aqueous, while the manometer is filled with mercury. As the aqueous solution is cooled down to 4C, its volume descreases, which in turn increases the volume of the air space above the solution. This reduces the gas pressure of the system (in addition to the drop in pressure associated with a lower temperature). With the pressure inside the flask dropping, the mercury in the manometer will shift to the side connected to the flask (in this case the left side). Does that make sense?
