Answer:
These energy exchanges are not changes in kinetic energy. They are changes in bonding energy between the molecules. "If heat is coming into a substance during a phase change, then this energy is used to break the bonds between the molecules of the substance
Kinetic energy means movement. This means that the more something moves, the more kinetic energy it will have! And the faster something moves, the more heat it produces! Altogether, this means that the more Kinetic energy something has, the hotter it will be!
The opposite is also true. The less something moves, it will have less Kinetic energy and the colder it will get.
If you're having trouble understanding this, think of it like how the particles in water move compared to how the particles in ice move. The particles in water are free flowing and can move wherever they want. If they get colder, they won't move as much, and eventually they'll stop flowing around, forming a solid and staying colder than the water will get.
1) 29.8 C
At the beginning, the metal is at higher temperature (70.4 C) while the water is at lower temperature (23.6 C). When they are put in contact, the metal transfers heat to the water, until they reach thermal equilibrium: at thermal equilibrium the two objects (the metal and the water have same temperature). Therefore, since the temperature of the water at thermal equilibrium is 29.8 C, the final temperature of the metal must be the same (29.8 C).
2) 6.2 C
The temperature change of the water is given by the difference between its final temperature and its initial temperature:

where

Substituting into the formula,

And the positive sign means that the temperature of the water has increased.
3) -40.6 C
The temperature change of the metal is given by the difference between its final temperature and its initial temperature:

where

Substituting into the formula,

And the negative sign means the temperature of the metal has decreased.