To eliminate the fractions in the equation \( \frac{1}{3}x + \frac{1}{6}y = 4 \), we need to find the least common multiple (LCM) of the denominators involved, which are 3 and 6.
The LCM of 3 and 6 is 6. Therefore, Rashonda should multiply the entire equation by 6 to clear the fractions.
Here’s the multiplication step:
\[ 6 \left( \frac{1}{3}x + \frac{1}{6}y \right) = 6 \cdot 4 \]
This results in:
\[ 2x + y = 24 \]
So, the answer is that she should multiply the equation by 6.