Answer
$\frac{3}{8}x^3y^4$
Work Step by Step
By multiplying the numerical coefficients and adding the powers of the variables, we get
$$\left(\frac{2}{3} x^{2} y^{2}\right)\left(\frac{9}{16} xy^{2}\right)=\frac{18}{48}x^3y^4=\frac{3}{8}x^3y^4.$$