32/4 pieces f cake after party eats 1 /2/3 next night how much does she have left

The person has 1 5/6 cake left because 3 2/4 - 1 2/3 = 1 5/6! Hope this helps ^0^

Explanation 
Rewriting Expression in different parts.
= 3 + 2/4 + 1 + 2/3.

Solving The Whole Number Parts.
3 + 1 = 4

Solving The Fraction Parts.
2/4 + 2/3 = ?

Find the LCD of 2/3 and 2/4 and Rewrite to solve with equivalent Fractions.
LCD = 12
6/12 + 8/12 = 14/12

Simplify the Fraction Part.
14/12 = 7/6

Simplify The Fraction Part Again.
7/6 = 1 1/6

Combining The Whole Numbers With The Fractions.
4 + 1 + 1/6 = 5 1/6 

Hope this helps ^0^! ;D