Question

What mass of ice at -14 degree Celsius will be needed to cool 200 cm of an orange drink from 25 degree Celsius to 10 degree? (specific latent heat of fusion of ice=336000,specific heat capacity of ice=2100 specific heat capacity of water=4200

Answer 1

Your nonuse of units on the heats is disappointing. I am going to guess they are in J/kg, even in that, they are rouned loosely.
The sum heat changes = zero.
-massice*2100J/kg-massice*336000J/kg -(massice)4200(10-0)+200(4200)(25-10)=0

check that. Negative means heat absorbed, positive means heat given off.

Answer 2

840g