Solution 1 - array lists are separate:
ArrayList big = new ArrayList();
big.Add(arraylist1);
big.Add(arraylist2);
big.Add(arraylist3);
big.Add(arraylist4);
Solution 2 - array lists are appended:
ArrayList big = new ArrayList();
big.AddRange(arraylist1.ToArray());
big.AddRange(arraylist2.ToArray());
big.AddRange(arraylist3.ToArray());
big.AddRange(arraylist4.ToArray());