The solution of \(8x+1\equiv 5 \pmod{12}\) is \(x\equiv a\pmod{m}\) for some positive integers \(m\geq 2\) and a
I guess you are trying to ask what is the values of m and a.
\(8x + 1 \equiv 5\pmod{12}\\ 8x\equiv4\pmod{12}\\ 8x\equiv16\pmod{12}\\ x\equiv2\pmod{12}\)