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Ensure that share root has "authenticated users" have full control share permissions
disable permissions inheritance on root share folder advanced NTFS permissions with convert explicit option
Then grant "authenticated users" List folder contents permissions on root share
Remove any explicit groups if defined here on ACL
Now go to "Eng-Part" folder and disable inheritance and change authenticated users permissions scope (Applied to) to this Folder Only
Then add required group required access here
This process to followed for all other groups
This will ensure that group members will able to access only folders for which they have access
Also you may enable access based enumeration on share folder so that folders get hide from explorer for which user do not have permissions
http://heineborn.com/tech/enable-access-based-enumeration-in-windows-server-2012/