A body is thrown vertically upwards. Its velocity keeps on decreasing. What happens to its kinetic energy when it reaches the maximum height?

The kinetic energy will rise once the body comes back down. As it goes up, the potential energy increases while the kinetic energy decreases. Once the body is at its maximum height, the potential energy is at it's highest. When it starts falling, it will gain kinetic energy and lose potential energy.

When it reaches the maximum height, it's not moving up any more, and it's getting ready to start moving down. In between, there's an instant there when it's not moving at all. Kinetic energy depends on speed. So at the instant it's not moving, it has no kinetic energy. Zero. Nada.