A hot iron ball is dropped into 200.0 g of cooler water. The water temperature increases by +2.0°C and the temperature of the ball decreases by -18.6°C. What is the mass of the iron ball?

Answer 1

heat lost by Fe ball + heat gained by H2O = 0

[mass Fe x specific heat Fe x (Tfinal-Tinitial_)] + [mass H2O x specific heat H2O x (Tfinal-Tinitial)] = 0
You don't know Tf and Ti but you can replace those with delta T which is 2 for H2O and -18.6 for Fe.