We start with the ratio given by Pooja:
\[ \frac{x}{3} = \frac{y}{4} \]
We can rewrite this equation as:
\[ x \cdot 4 = y \cdot 3 \] or \[ 4x = 3y \]
Now, we are given that \(x\) is 15 units. We can substitute this value into the equation:
\[ 4(15) = 3y \]
Calculating the left side:
\[ 60 = 3y \]
To find \(y\), we can divide both sides by 3:
\[ y = \frac{60}{3} = 20 \]
Thus, the value of \(y\) is
\[ \boxed{20} \]