First, let's find the price of the dress after 25% discount is applied. 25% is also equal to 0.25, so:
[tex]32*0.25 = 8[/tex]
[tex]32-8=24[/tex]
The dress costs $24 after discount. Since Nicole's mom will pay for half of that, this means that mom will pay $12. This leaves $12 of the dress that Nicole has to pay.