A: Hello,Roger.This is Ann.
B: Hi,Ann.Where have you been? And how's your new apartment working out?
A: Well, that's what I'm calling about.I've decided to look for a new place that have a part.Can you help me?
B: OK,I will make a couple of phone calls and get back to you later.
A: thanks.
work out 在这儿是什么意思 How's your new apartment working out 是什么意思
I'll make a couple of phone calls是什么意思

---你好，罗杰，我是安
---你好，安。最近去那里了？你的新公寓怎么样了？
---这就是我打电话的原因。我想找个新的带？（这里have a part不解）的公寓，你能帮我吗？
---好的，我打几个电话问问看，一会儿给你打电话。
---谢谢。

work out 在这里应该是指装修或者是搬家什么的，意译为“怎么样”；How's your new apartment working out 是问安的新公寓进展如何；I'll make a couple of phone calls是“我打几个电话（帮你问问看）”