This problem is a bit uncharacteristic for related rates - but here goes!
If V = (pi/3)*x^2y given V = 96pi then
x^2y = 288 now differentiate implicitly keeping in mind both the product and chain rule!!
d/dx (x^2y = 288) = 2xy + x^2(dy/dx) = 0
Now plug in x and y
2(6)(8) + 36(dy/dx) = 0
36(dy/dx) = - 96
dy/dx = -96/36