To find the ratio of X to Z, we can use the concept of equivalent ratios.

Given that the ratio of X to Y is 3/4 and the ratio of Y to Z is 12/13, we can set up the proportion:

(X/Y) = (3/4) and (Y/Z) = (12/13)

To find the ratio of X to Z, we need to eliminate Y from the equation. To do this, we can multiply both equations together:

(X/Y) * (Y/Z) = (3/4) * (12/13)

By canceling out the Y terms, we are left with:

X/Z = (3/4) * (12/13)

Multiplying the numerators and denominators, we get:

X/Z = 36/52

Simplifying the fraction, we have:

X/Z = 9/13

Therefore, the ratio of X to Z is 9/13, which corresponds to option 4.