Respuesta :

It would have been clearer had you written, 

"How would I solve     'z divided by 4/9 equals 3/8' ?

You meant

 z
--------   = 3/8, or     9z/4 = 3/8.
   4
   --
    9

The LCD here is 8.  Mult. both sides by 8:  18z = 3.

Solve this last result for z:    z = 3/18, or           z = 1/6   (answer)