高夫先生坚信可以用快速转移到新试题推介并呼吁家长和雇员支持他的方式来赢得这场争论.
appling 与moving 是并列的,都是is banking on的宾语.
主要的分辨依据是：他们都是winning argument的方式.
假设appealing与banking是并列的,就变成了：他坚信.他正在呼吁.
这句话就不协调了.
所以,他用...moving .和appealing 两种方式是比较好的选择,于情于理都说得通.
bank on something - 这是个词组.有如下意思：rely on,trust (in),depend on,look to,believe in,count on,be sure of,lean on,be confident of,have confidence in,swear by,reckon on,repose trust in.
举例：She is clearly banking on her past to be the meal ticket for her future.她清楚地知道她的过去就是她未来的饭票.