If a, b, and c are positive integers less than 13 such that

2*a*b + b*c + c*a == 0 (mod 13)

a*b + 2*b*c + c*a == 4*a*b*c (mod 13)

a*b + b*c + 2*c*a == 8*a*b*c (mod 13)

then determine the remainder when a+b+c is divided by 13.

Did you check your first post? Look under it.