What is incorrect about this problem? -1/4 divided by 3/2 = -4/1 times 3/2 =-12/2 = -6

First of all, I'd suggest that you use a new, clean, blank line for every bit of new information.

-1/4 divided by 3/2 = -4/1 times 3/2     Do NOT insert another " = " sign here, but move on to a new line.  

"-1/4 divided by 3/2 = -4/1 times 3/2 =-12/2 = -6"

You are dividing -1/4 by 3/2.  To do this, invert 3/2 and then multiply:

-1       2
* = -1/6
 4        3

Notice how I have only ONE " = " sign here.