To solve the equation \( 7(x - 6) = 4x + 9 \), follow these steps:

1. Distribute the \( 7 \) on the left side:
\[
7x - 42 = 4x + 9
\]

2. Move the \( 4x \) from the right side to the left side by subtracting \( 4x \) from both sides:
\[
7x - 4x - 42 = 9
\]
\[
3x - 42 = 9
\]

3. Add \( 42 \) to both sides to isolate the term with \( x \):
\[
3x = 9 + 42
\]
\[
3x = 51
\]

4. Divide both sides by \( 3 \) to solve for \( x \):
\[
x = \frac{51}{3}
\]
\[
x = 17
\]

So, the solution is \( x = 17 \).