is this the correct way to find specific heat
 

it might be a little differnt then the actual book equation but is this correct?

Specific Heat= heat capacity/mass

To find the heat capacity: Heat Capacity= quantity (J)/delta T
delta T=(final temp/initial temp)

I found the specific heat for water as follows:
Heat capacity= 67200J/57.7-22 deg C
= 1882.352941 J/deg C

Specific Heat= 1882.352941 J/deg C / 459 g
Specific Heat= 4.1009868

I see no problem in your method and the answer is only very slightly off what we were told in Physics, so I would assume its fine.