Given that x : y : z = 3 : 3 : 4, we can say that x = 3k, y = 3k, and z = 4k for some constant k.

We are asked to evaluate \[\frac{9x + 3y}{6x - 2y}.\]

Substitute x = 3k and y = 3k into the expression:

\[\frac{9(3k) + 3(3k)}{6(3k) - 2(3k)} = \frac{27k + 9k}{18k - 6k} = \frac{36k}{12k} = 3.\]

Therefore, the correct answer is 3.