Answer: \(m = 14\)
\(a = m - 12, b = 2(m - 12), c = 2\). Real and equal roots: \(b^2 - 4ac = 0\).
\[4(m - 12)^2 - 8(m - 12) = 0\]\[4(m - 12)(m - 12 - 2) = 0\]\[4(m - 12)(m - 14) = 0\]\(m = 12\) or \(m = 14\). If \(m = 12\), \(a = 0\) and the equation is not quadratic, so \(m = 14\).