For which phase change does water absorb the most energy?
If we are considering melting and boiling, the clear choice is boiling, which requires almost 7 times more energy than melting.
The numbers you want are called the molar heat of fusion, which gives us the energy needed to cause melting (at the melting point, without change in temperature). For water, this is
You also want to molar heat of vapourization, which is the energy needed for the liquid to vapour change. For water, this is
So, for water, vapourization requires 6.8 times as much energy compared to melting.