The custom search limit is used in finalGoal. The solution counter used by the search limit only increments if the sixth car in the sequence is green. When the solution counter reaches the search limit, the search is stopped.

    IloSolver solver(model);
    IloGoal goal = IloGenerate(env, cars, IloChooseMinSizeInt);
    IloInt counter=0;
    IloSearchLimit limit = IloMyLimit(env, counter, 2);
    IloGoal finalGoal = IloLimitSearch(env, goal, limit);
    solver.startNewSearch(finalGoal);
    while (solver.next())
      {
      solver.out() << solver.getStatus() << " Solution" << endl;
      if (solver.getValue(cars[5]) == 0) { // Car 6 is green
        for (i = 0; i < nbCars; i++) {
          solver.out() << "Car " << i+1 <<  " color:     "
                       << Names[(IloInt)solver.getValue(cars[i])]
                       << endl;
        }
        counter++;
      }
    }
      solver.endSearch();