Given that 

\(\frac{a}{b} = \frac{c}{d} = k\)

we can express \(a\) and \(c\) as:

\(a = kb, \quad c = kd\)

We want to find the value of 

\(\frac{3a^2 - ac + c^2}{3b^2 - bd + d^2}\)

Substituting \(a\) and \(c\) into the expression gives:

\(3a^2 - ac + c^2 = 3k^2b^2 - k^2bd + k^2d^2 = k^2(3b^2 - bd + d^2)\)

Thus, the expression simplifies to:

\(\frac{k^2(3b^2 - bd + d^2)}{3b^2 - bd + d^2} = k^2\)

Therefore, the value is: \(k^2\)