A hot iron ball is dropped into 200g of cooler water. The water temperature increases by 2.0 degrees C and the temperature of the ball decreases by18.6 degrees C. What is the mass of the ball

Answer 1

mass ball x specific heat Fe x (Tfinal - Tinitial) + mass H2O x specific heat H2O x (Tfinal - Tinitial) = 0
mass ball x specific heat ball x (-18.6) + 200 x specific heat H2O x (2)
Look up specific heat Fe and specific heat H2O, substitute those numbers and solve for mass Fe ball.
Post your work if you get stuck.