Answer: \(\frac{7}{18}\)
Let the numerator be \(x\) and the denominator be \(y\).
First condition: \(y = 2x + 4\), i.e. \(2x - y = -4\) ... (I)
Second condition: \(y - 6 = 12(x - 6)\), so \(y - 6 = 12x - 72\), i.e. \(12x - y = 66\) ... (II)
Subtract (I) from (II): \(10x = 70\), so \(x = 7\). Then \(y = 2(7) + 4 = 18\).
Check: \(\frac{18 - 6}{7 - 6} = 12\), which is true. The fraction is \(\frac{7}{18}\).