The water in the two beakers is mixed. What is the final water temperature?

Let T°C be the final water temperature, and c be the specific heat capacity of water.
Heat change = m c ΔT

Heat absorbed by water at 23°C = Heat released from water at 93°C
157 × c × (T - 23) = 51.7 × c × (93 - T)
157 × (T - 23) = 51.7 × (93 - T)
157T - 157 × 25 = 51.7 × 93 - 51.7T
157T + 51.7T = 51.7 × 93 + 157 × 23
208.7T = 51.7 × 93 + 157 × 23
T = (51.7 × 93 + 157 × 23)/208.7
T = 40

Final water temperature = 40°C