Chemistry Calorimetry Problem?

I think you probably started with a hot piece of metal dropped into water, so the DeltaT for the water and the DeltaT for the metal won't be the same. DeltaT for the metal is Tfinal-Tinitial, where Tfinal the same as the final temp of the water, but Tinitial will be some higher temp. Other than that, you are doing the problem correctly. Watch the sign. Your DeltaT for the metal will come out negative (hot going to cold), but don't worry about that. Your specific heat capacity answer needs to be a positive number.