ok, your sketch doesn't do much at the moment - no drawing or anything.

the reference says:

"When using an array of objects, the data returned from the function must be cast to the object array's data type. For example: SomeClass[] items = (SomeClass[]) append(originalArray, element)."

which is your problem. that line should be "sticks = (Stick[])append(sticks, x);"

BUT SticksGroup looks like it's just a group of sticks. i'd use java's ArrayList class, which is a resizeable array and one that's standard and has been debugged 8)

http://download.oracle.com/javase/1.5.0/docs/api/java/util/ArrayList.html

1. int w = 240;
2. int h = 240;
3. ArrayList<Stick> sticks = new ArrayList<Stick>();
4.   
5. void setup() {
6.   size(w, h);
7.   smooth();
8.   // add initial stick
   
9.   sticks.add(new Stick(int(random(w)), int(random(h)), int(random(w)), int(random(h))));
10. }
11. 
    
12. void draw() {
13.   background(204);
14. }


15. class Stick{
16.   int x1, y1, x2, y2;
17.   Stick(int tempx1, int tempy1, int tempx2, int tempy2) {
18.     x1 = tempx1;
19.     y1 = tempy1;
20.     x2 = tempx2;
21.     y2 = tempy2;
22.   }
23.   void update() {
24.     line(x1, y1, x2, y2);
25.   }
26. }