In your screenshot - you have enabled package permissions. Looks like the permissions should enable the user to install packages. Typically however - users (authros) should not have package permissions - this should be an admin task.
Agreeing with Scott, It is consider as best practice to allow administrators users to install the packages.
If you look at the access properties of administrators group, you will see that it has all the access checked for package folder. Whereas if we consider content-author group whose role is for content editing, do not have access rights for package.
I would request you to please have a look at this documentation :- https://docs.adobe.com/docs/en/aem/6-2/administer/security/security.html
and also have a look at the permission access for these groups in http://localhost:4502/useradmin
I repeat my Question, may be some were i was not able to explain my requirement.
DEV team need user, who has read permission to Packmgr and creating package. That user should not be able install replicate or delete a package.
Permission which I have given seems to be working.