## To simplify the expression (12x^2y^3/2xy^2 + 6xy) * (y^2 + 6y + 9)/(3y^3 + 9y^2), we can break it down into smaller steps:

Step 1: Simplify the first fraction:

The numerator of the first fraction is 12x^2y^3, and the denominator is 2xy^2. To simplify, we can cancel out common factors. Canceling out y^2 and xy from the numerator and denominator respectively, we get:

(12x^2y^3)/(2xy^2) = (12x^2y^3)/(2xy^2) = (6x)/1

Step 2: Simplify the second fraction:

The second fraction is (y^2 + 6y + 9)/(3y^3 + 9y^2). This expression cannot be further simplified.

Step 3: Combine the simplified fractions:

Now, we have (6x)/1 * (y^2 + 6y + 9)/(3y^3 + 9y^2).

So, the simplified expression is (6x(y^2 + 6y + 9))/(3y^3 + 9y^2).

Note: This is simply a simplification of the given expression. If you were looking to solve an equation or find a specific value for x and y, you would need additional information or context.