La'Shondra starts with the inequality:
\[ 6 + 3x \leq 24 \]
First, she subtracts 6 from both sides:
\[ 3x \leq 24 - 6 \] \[ 3x \leq 18 \]
Next, to isolate \( x \), she divides both sides by 3:
\[ x \leq \frac{18}{3} \] \[ x \leq 6 \]
Therefore, the number she divides by is 3.