This is a quite easy redox reaction, which can be split into two steps. The fiirst one is a double exchange reaction
Cu(NO3)2 + 2KI = CuI2 + 2KNO3
The next step is a redox one
2CuI2 = 2CuI + I2
After joining both reaction together (with proper coefficients):
2Cu(NO3)2 + 4KI =