def sum_except_between_6_and_9(sequence):
    """
    :param sequence: a list of numbers
    :return: the sum of numbers excluding those between 6 and 9
    """
    if 6 not in sequence or 9 not in sequence:
        # 如果数列中没有6或9，直接返回所有数字之和
        return sum(sequence)
    
    # 找到6和9第一次出现的位置
    start_index = sequence.index(6)
    end_index = sequence.index(9)
    
    # 判断6和9的位置关系
    if start_index < end_index:
        # 如果6在9前面，删除6到9之间的数
        del sequence[start_index:end_index+1]
    else:
        # 如果9在6前面，则需要反转数列，再做同样的操作
        sequence.reverse()
        start_index = sequence.index(6)
        end_index = sequence.index(9)
        del sequence[start_index:end_index+1]
        sequence.reverse()
    
    # 计算除6和9之间的数字之和
    return sum(sequence)

示例：

>>> sum_except_between_6_and_9([1, 2, 3, 4, 5, 6, 7, 8, 9])
15
>>> sum_except_between_6_and_9([1, 2, 3, 4, 5, 7, 8, 9])
29
>>> sum_except_between_6_and_9([1, 2, 3, 6, 7, 9, 4, 5, 8])
15
>>> sum_except_between_6_and_9([1, 2, 6, 3, 4, 5, 7, 8, 9])
6