A piece of unknown metal with mass 68.6 g is heated to an initial temperature of 100 °C and dropped into 8.4 g of water (with an initial temperature of 20 °C) in a calorimeter. The final temperature of the system is 52.1°C. The specific heat of water is 4.184 J/g*⁰C. What is the specific heat of the metal?

[mass metal x specific heat metal x (Tfinal-Tinitial)] + [mass H2O x specific heat H2O x (Tfinal-Tinitial)] = 0

Plug in and solve for specific hat metal. You have values for the other components. Post your work if you get stuck
mass metal = 68.6 g
sp. H. metal = ?
Tfinal metal = 52.1 C
Tinitialmetal = 100 C
mass water = 8.4 g
specific heat H2O = 4.184
Tfinal H2O = 52.1 C
TinitialH2O = 20 C