vim, 209 bytes

Result

AC

Duration

526ms

Code [DL]

VGJ:let l=map(split(getline(1),' '),'str2nr')
:for i in range(9)
let l[i+3]-=l[i%3]
endfor
:call setline(1, (l[3]*l[7]*l[11]+l[6]*l[10]*l[5]+l[9]*l[4]*l[8]-l[5]*l[7]*l[9]-l[8]*l[10]*l[3]-l[11]*l[4]*l[6])/6)
ZZ

Disassembly

VGJ:let l=map(split(getline(1),' '),'str2nr')<NL>:for i in range(9)<NL>let l[i+3]-=l[i%3]<NL>endfor<NL>:call setline(1, (l[3]*l[7]*l[11]+l[6]*l[10]*l[5]+l[9]*l[4]*l[8]-l[5]*l[7]*l[9]-l[8]*l[10]*l[3]-l[11]*l[4]*l[6])/6)<NL>ZZ

stdin

69 94 05
02 30 32
03 19 05
47 10 03

stdout

17256

stderr

strace