Answer
See the detailed answer below.
Work Step by Step
To answer this question, let's have a look at the water phase diagram in Figure 16.4 in your textbook.
a) We know that as the piston squeezes the vapor, the pressure increases. The increase in pressure increases the temperature and both of them make the vapor converts to liquid as shown in Figure 16.4.
Noting that it starts at $-0.01^\circ\rm C$
With continuous pushing by the piston, the pressure increases, and the temperature increases, and that pushes the water to convert to the ice for a while then with the increase of both, the pressure and the temperature, it converts to liquid again.
b) Now, in this case, we start at $T=0.03^\circ \rm C$, which means that the vapor will not move to the solid state, but finally, we got the same result, the whole sample will be converted to a liquid.
