The problem is to evaluate the expression $\frac{12\sqrt{2}}{\sqrt{16}\sqrt{18}}$.

1. Problem Description

The problem is to evaluate the expression $\frac{12\sqrt{2}}{\sqrt{16}\sqrt{18}}$.

2. Solution Steps

First, we can simplify the expression by writing the denominator as a single square root:

$\frac{12\sqrt{2}}{\sqrt{16}\sqrt{18}} = \frac{12\sqrt{2}}{\sqrt{16 \cdot 18}}$.

Now we compute the product inside the square root in the denominator: $16 \cdot 18 = 288$.

So we have $\frac{12\sqrt{2}}{\sqrt{288}}$.

Now we simplify $\sqrt{288}$. Since $288 = 144 \cdot 2 = 12^2 \cdot 2$, we have $\sqrt{288} = \sqrt{144 \cdot 2} = \sqrt{144} \cdot \sqrt{2} = 12\sqrt{2}$.

Substituting this back into the original expression gives $\frac{12\sqrt{2}}{12\sqrt{2}}$.

Since the numerator and denominator are the same, the expression simplifies to

1.

3. Final Answer

1