What is the specific heat of a substance if 1560 cal are required to raise temperature of a 312 g substance by 15 degrees celsius?

The Specific Heat formula is: 
  c = ΔQ / (m × ΔT)

Where:
  c: Specific Heat , in J/(kg.K)
  ΔQ: Heat required for the temperature change, in J
  ΔT: Temperature change, in K
  m: Mass of the object, in kg

So substitute the numbers in; Calories should be converted into joules
c = 1560(4.184)/(312*15)
c = 1394.666