Step 1: link boiling to escaping vapour.
A liquid boils when its vapour pressure climbs up to match the air pressing on it. So anything that makes the liquid give off vapour more easily lowers the boiling point, and anything that holds the vapour back raises it. The two solutes here pull this in opposite directions.
Step 2: why KCl pushes the boiling point up.
KCl cannot evaporate at all; it is a non-volatile salt. When it dissolves, its ions sit among the water molecules and hold some of them back from escaping into vapour. With fewer water molecules leaving, the vapour pressure of the solution drops below that of pure water. To make up for this and reach boiling, the solution must be heated to a higher temperature, so the boiling point rises.
Step 3: why methanol pulls the boiling point down.
Methyl alcohol is the opposite kind of solute. It is itself quite volatile, even more eager to escape than water. So it adds its own vapour on top of the water's vapour, and the total vapour pressure of the mixture goes up above that of pure water. Since vapour pressure is reached sooner now, a lower temperature is enough to boil it, so the boiling point falls.
KCl (non-volatile) raises the boiling point; methanol (volatile) lowers it.