To solve the inequality \( 6 + 3x \leq 24 \), La'Shondra begins by subtracting 6 from both sides:
\[ 6 + 3x - 6 \leq 24 - 6 \] which simplifies to:
\[ 3x \leq 18 \]
Next, she needs to isolate \( x \) by dividing both sides of the inequality. The number she divides by is 3.
So, the answer is 3.