To find the missing factor \( G \) in the equation
\[ 18y^3 = G(2y^2), \]
we can start by isolating \( G \). We can do this by dividing both sides of the equation by \( 2y^2 \):
\[ G = \frac{18y^3}{2y^2}. \]
Now we can simplify the right side. First, we simplify the numerical portion:
\[ \frac{18}{2} = 9. \]
Next, regarding the variable part, we can simplify \( y^3/y^2 \) using the rule of exponents that states \( \frac{y^m}{y^n} = y^{m-n} \):
\[ \frac{y^3}{y^2} = y^{3-2} = y^1 = y. \]
Putting this all together, we find:
\[ G = 9y. \]
Thus, the missing factor \( G \) is
\[ \boxed{9y}. \]