To solve the inequality
\[ \frac{3(x - 6)}{2} \geq \frac{2x}{7} - 12, \]
first, we clear the fractions by multiplying both sides by 14 (the least common multiple of 2 and 7):
\[ 14 \cdot \frac{3(x - 6)}{2} \geq 14 \cdot \left(\frac{2x}{7} - 12\right). \]
This simplifies to:
\[ 7 \cdot 3(x - 6) \geq 4x - 168. \]
Now simplify the left side:
\[ 21(x - 6) \geq 4x - 168. \]
Distributing 21 gives us:
\[ 21x - 126 \geq 4x - 168. \]
Next, isolate \(x\) by subtracting \(4x\) from both sides:
\[ 21x - 4x - 126 \geq -168. \]
This simplifies to:
\[ 17x - 126 \geq -168. \]
Now add \(126\) to both sides:
\[ 17x \geq -168 + 126. \]
Calculating the right side yields:
\[ 17x \geq -42. \]
Finally, divide both sides by 17:
\[ x \geq -\frac{42}{17}. \]
Thus, the solution to the inequality is
\[ x \geq -\frac{42}{17}. \]