#### Answer

$(\frac{4x^{2}}{3y})$

#### Work Step by Step

Since dividing fractions is not possible, we need to flip the fraction to the right of the division sign in order to replace the division sign with the multiplication sign. Then, we simplify the fractions by cancelling out common factors.
Step 1: $(\frac{6x^{2}y}{11})\div(\frac{9y^{2}}{22})$
Step 2: $(\frac{6x^{2}y}{11})\times(\frac{22}{9y^{2}})$
Step 3: $(\frac{6x^{2}y}{1})\times(\frac{2}{9y^{2}})$
Step 4: $(\frac{6x^{2}}{1})\times(\frac{2}{9y^{2-1}})$
Step 5: $(\frac{6x^{2}}{1})\times(\frac{2}{9y})$
Step 6: $(\frac{2x^{2}}{1})\times(\frac{2}{3y})$
Step 7: $(\frac{4x^{2}}{3y})$