I would appreciate it___you call back this afternoon for the doctor's appoinment.

很简单,把这句话拆成两部分来看：
第一部分：I would appreciate it
第二部分：if you call back this afternoon for the doctor's appointment
第二部分不是第一部分的宾语或者定语（否则的话,有可能用that连接）,两部分是并列的,也可以简单理解为一个 If ...,I will/ would ...“如果⋯⋯,我就⋯⋯”的条件结构,再比如：
I would be grateful if you could open it for me.如果你能帮我打开的话,我会感激不尽.
It would be great if you could make it.如果你能来的话,那就太好了.