How do you solve/simplify

32x^3y^4. 3X
Over. Times
24x^3y^2. 9Y

If you mean

(32x^3y^4)/(24x^3y^2) * (3x)/(9y)

multiply top and bottom to get

(96x^4y^4)/(216x^3y^3)
= (24x^3y^3)(4xy) / (24x^3y^3)(9)
= 4xy/9

Or, you could simplify each fraction first, getting
(8x^3y^2)(4y^2) / (8x^3y^2)(3) * (3)(x)/(3)(3y)
= 4y^2/3 * x/3y = 4xy/9