To solve the equation \( 4(2x - 3) = 5x + 6 \), we can start by distributing the 4 on the left-hand side:
\[ 4 \cdot 2x - 4 \cdot 3 = 5x + 6 \] \[ 8x - 12 = 5x + 6 \]
Next, we can isolate \( x \) by moving all terms involving \( x \) to one side and constant terms to the other side. Subtract \( 5x \) from both sides:
\[ 8x - 5x - 12 = 6 \] \[ 3x - 12 = 6 \]
Now, add 12 to both sides:
\[ 3x = 6 + 12 \] \[ 3x = 18 \]
Finally, divide by 3:
\[ x = \frac{18}{3} \] \[ x = 6 \]
Thus, the solution to the equation \( 4(2x - 3) = 5x + 6 \) is:
\[ \boxed{6} \]
So, the correct response is \( x = 6 \).