csharp, 337 bytes

Result

AC

Duration

815ms

Code [DL]

using System;using System.Linq;class A{static void Main(){string s="";for(int i=4;i>0;i--){s+=Console.ReadLine()+" ";}int[] a=s.Split(' ').Take(12).Select(Int32.Parse).ToArray();foreach(int z in Enumerable.Range(0,9)){a[z]-=a[9+z%3];}Console.Write(-(a[7]*(a[3]*a[2]-a[0]*a[5])+a[6]*(a[1]*a[5]-a[4]*a[2])+a[8]*(a[0]*a[4]-a[3]*a[1]))/6);}}

stdin

01 64 37
73 88 81
12 38 52
44 36 40

stdout

12492

stderr

strace