To find the value of \( z \), we recognize that \( 156^\circ \) and \( (12z)^\circ \) have a relationship that is often found in geometry, possibly indicating they are angles that either sum to 180° (if they are supplementary) or equate (if they are equal).
Given that we only have the two angles, and no indication in your question of one being supplementary or equal to the other, let’s assume they are equal (since that's a common problem setting).
Setting them equal gives:
\[ 12z = 156 \]
To solve for \( z \), divide both sides by 12:
\[ z = \frac{156}{12} \]
Calculating that gives:
\[ z = 13 \]
Thus, the value of \( z \) is:
\[ z = 13^\circ \]