How to find a user's mapped drives when I only have a copy of their c: drive

Load the registry hive from the old C:
navigate to HKEY_CURRENT_USER\Network
There will be sub-folders for each drive under the letter used for the mapping (So for X: look under HKEY_CURRENT_USER\Network\X\)
Look for the Value Name "Remote Path" which will contain the UNC path to the mapping.

Note, if no results are returned above the user doesn't have any mapped drives that they have set to "Reconnect at logon".

If you know the user had a mounted drive that was not set to automatically re-connect when you took the image of their hard drive you can find out most of the details for it here:

REG QUERY "HKU\TempUser\Software\Microsoft\Windows\CurrentVersion\Explorer\Map Network Drive MRU" /S

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I don't physically have the drive I only have access to a web based copy of the c: drive folders and files.  See attached "folders.docx".  So, I cannot go into the Registry of the c: drive.
folders.docx

Please just post images instead of Word documents in the future.

It looks like that is the user directory, which is where the user's NTUser.Dat file will exist.

So if you see the NTUser.dat file download it to your hard disk and use that location in the commands I provided.

Otherwise you cannot get the information you desire.

If you have (or can download) the NTUSER.DAT file you can do this as described above. If you only have access to the file names you cannot.

http://www.bluecompute.co.uk/blogposts/registry-tricks-editing-another-users-registry-entries/

Have a look for the above about remote registry edit.

Thanks, it worked

Glad to help!  :)