To clear the fractions from the equation \( y = \frac{2}{3}x + \frac{1}{4} \), we need to find a common multiple of the denominators (3 and 4) in the fractions.
The least common multiple (LCM) of 3 and 4 is 12.
Now, if we multiply every term in the equation by 12, we will eliminate the fractions:
\[ 12y = 12 \left(\frac{2}{3} x\right) + 12 \left(\frac{1}{4}\right) \]
This simplifies to:
\[ 12y = 8x + 3 \]
Therefore, the number Rahul can multiply the equation by to clear the fractions is:
\[ \boxed{12} \]