Simplify the algebraic expression: 2y / (3n2y * 18n4y)

The expression to simplify is:

$$\frac{2y}{3n^2y \cdot 18n^4y}$$

Multiply the numerical coefficients and combine the variables using the rule $a^x \cdot a^y = a^{x+y}$.

$$3n^2y \cdot 18n^4y = (3 \times 18) \cdot (n^2 \cdot n^4) \cdot (y \cdot y)$$ $$= 54n^{2+4}y^{1+1}$$ $$= 54n^6y^2$$

Divide the numerical coefficients: $\frac{2}{54} = \frac{1}{27}$.
Cancel the variable $y$: $\frac{y}{y^2} = \frac{1}{y}$.

$$\frac{1}{27n^6y}$$