Let x,y,z be positive integers.
Then number of solutions = 14C2=91
But x,y,z can be negative too.
So, total number of solutions (none of x,y,z is zero) is 91×2×2×2=728 ...(1)
Let one of x,y,z is equal to zero.
Then number of possible solutions = 14C1=14
But other two can be negative (14×2×2) and one of three can be zero.
Hence, number of solutions =14×2×2×3=168 ...(2)
Let two of x,y,z is zero, then number of solutions is 6 ...(3)
Adding (1),(2) and (3)
Total number of integral solutions, k = 902