Answer
Methane will freeze, changing from a liquid to a solid.
Work Step by Step
We are told that temperature is constant while the pressure will increase. We found in problem 11.63a that methane is generally liquid on Titan. Because the temperature increases, but the pressure does not change, we imagine a vertical line where the temperature remains a constant -178 degrees Celcius. At the upper part of this line, where pressure is higher, we see that methane is a solid, meaning that methane changes from a liquid (like it is originally, which we found in 11.63a) to solid.
