To determine the correct equation to solve for \( x \), we start from the fact that supplementary angles sum to \( 180^\circ \). The angles provided are:
\[ \angle MAT = (6x - 6)^\circ \] \[ \angle TAH = (4x - 14)^\circ \]
Since these angles are supplementary, we can set up the equation:
\[ (6x - 6) + (4x - 14) = 180 \]
Now simplify the left side:
\[ 6x - 6 + 4x - 14 = 180 \] \[ 10x - 20 = 180 \]
Thus, the correct equation to solve for \( x \) is:
\[ 10x - 20 = 180 \]