vim, 199 bytes

Result

WA

Duration

529ms

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[11]*(l[7]*l[3]-l[4]*l[6])+l[10]*(l[5]*l[6]-l[3]*l[8])+l[9]*(l[4]*l[8]-l[7]*l[5]))/6)
ZZ

Disassembly

<NL>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[11]*(l[7]*l[3]-l[4]*l[6])+l[10]*(l[5]*l[6]-l[3]*l[8])+l[9]*(l[4]*l[8]-l[7]*l[5]))/6)<NL>ZZ

stdin

20 58 19
51 13 78
11 45 06
69 97 15

stdout

20 58 19
51 13 78 11 45 06 6
 97 15

stderr

strace