Evaluate the double integral.
\[
\int_{1}^{2} \int_{3 y}^{6 y} \frac{2}{x} d x d y
\]
\[
\int_{1}^{2} \int_{3 y}^{6 y} \frac{2}{x} d x d y=\square \text { (Type an exact answer.) }
\]

Step 1 ：The given integral is a double integral. The inner integral is with respect to x and the outer integral is with respect to y. The limits of the inner integral are functions of y (3y to 6y) and the limits of the outer integral are constants (1 to 2). The integrand is a function of x only.

Step 2 ：To solve this double integral, we first need to solve the inner integral. The integral of \(\frac{2}{x} dx\) is \(2\ln|x|\). We will evaluate this from 3y to 6y.

Step 3 ：Then we will take this result and integrate it with respect to y from 1 to 2.

Step 4 ：The result of the inner integral is \(-2\ln(3y) + 2\ln(6y)\).

Step 5 ：The result of the double integral is \(-2\ln(3) + 2\ln(6)\).

Step 6 ：The final answer is a numerical value. We can simplify the expression \(-2\ln(3) + 2\ln(6)\) to get the final answer.

Step 7 ：The final answer is \(\boxed{\log(4)}\).