Writer initialization failed.Error opening output file.The system cannot find the path specified

It's exactly as it says: the Writer failed to initialize, as it was not able to locate the path and file specified.

Note that PowerCenter Workflows and Mappings are executed on the Server. So while you develop on your local laptop (for example) and place a file in C:\Temp folder, and you are able to see the file, once you run the process, it will be executed on the Server. And the Server will not refer your laptop. It will look for C:\Temp location on its local disk. And if that's a unix box, there won't even be a C: path!

Hence, the process will fail with exactly the message you've seen: initialization failed, error opening output file. You need to place the file in the location accessible by Server.

In case of Writer, you name target location where the file will be created - make sure the user used by PowerCenter does have the write access.