To solve the equation \( 9(k - 7) = 6k \), we will start by expanding the left side:
\[ 9(k - 7) = 9k - 63 \]
Now, the equation becomes:
\[ 9k - 63 = 6k \]
Next, we can isolate the terms involving \( k \) by subtracting \( 6k \) from both sides:
\[ 9k - 6k - 63 = 0 \]
This simplifies to:
\[ 3k - 63 = 0 \]
Next, we add 63 to both sides:
\[ 3k = 63 \]
Now, we can find \( k \) by dividing both sides by 3:
\[ k = \frac{63}{3} = 21 \]
Thus, the solution for \( k \) is:
\[ \boxed{21} \]