\[x^{2} - (a - 6)x + 4 = 0\]
\[D = a^{2} - 12a + 36 - 16 = a^{2} - 12a + 20\]
\[a^{2} - 12a + 20 < 0\]
\[a_{1} + a_{2} = 12,\ \ a_{1} \cdot a_{2} = 20\]
\[a_{1} = 2,\ \ a_{2} = 10\]
\[(a - 2)(a - 10) < 0\]
\[2 < a < 10.\]
\[Ответ:(2;10).\]