Let the current ages of Anna, Ben, and Chloe be denoted as $A$, $B$, and $C$, respectively.

Step 1: Set up the given relationships as equations.

1. The sum of their ages is 96: $A + B + C = 96$
2. Anna is twice as old as Ben: $A = 2B$
3. Ben is 4 years older than Chloe: $B = C + 4$
4. In 8 years, Anna will be three times as old as Chloe was 4 years ago: $A + 8 = 3(C - 4)$

Step 2: Solve the system of equations.

We have the system of equations:

1. $A + B + C = 96$