(20.0) (165.0 - x) (0.14) = (200.0) (x - 60.0) (4.18)

Noting that 200/20 = 10, I get:

23.1 - 0.14x = 41.8x - 2508

41.94x = 2531.1

x = 60.35 °C

Note that the water moves only 0.35 of one degree. Keep in mind that there is a large amount of water compared to the mercury AND that it takes a great deal more energy to move water one degree as compared to the same amount of mercury moving one degree.